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Conjoint Professor John Rayner

Conjoint Professor

School of Mathematical and Physical Sciences (Statistics)

Career Summary

Biography

During my career I have had significant administrative responsibilities that have reduced the time available for research. For example I was: President of the N.S.W. Branch of the Statistical Society of Australia from March 2002 to March 2004, and Council Member from March 1995 to March 1998 and March 1999 to 2006; Foundation Head of the Department of Applied Statistics at the University of Wollongong from January 1993 to December 1995; Foundation Head of the School of Mathematics and Applied Statistics at the University of Wollongong from July 1997 to June 2000; Coordinator of the Data Interpretation and Financial Analysis Program within the Institute of Mathematical Modelling and Computer Systems for 2001, Faculty of Informatics Faculty Research Committee Chair Autumn session 2002 and Director of the Institute of Mathematical Modelling and Computational Systems for 2002 and 2003, all substantive research management positions at the University of Wollongong; Head of the Statistics discipline at the University of Newcastle from my appointment here in February 2006. As Statistics Area Editor of the Journal Applied Mathematics and Decision Sciences I have published in my 'own' journal to support it. Similarly I have edited and published in proceedings of local/small workshops that I helped organise. The main goal here was to support early career and local researchers, not unnecessarily inflate my own output.

Research Expertise
My areas of research expertise are goodness of fit (statistical model assessment) and nonparametric statistics (that makes minimal modelling assumptions). I have published prolifically with quality publishers and in quality journals, including Chapman & Hall/CRC, Oxford University Press, Biometrika, Biometrics, Technometrics, Statistics and Probability Letters, and Communications in Statistics. My publications include over 110 articles in refereed journals, book chapters, conference proceedings and encyclopedias, four significant co-editorships and five books. In goodness of fit I have written over 40 articles for refereed journals, book chapters, conference proceedings and encyclopedias. Recently an anonymous reviewer of a journal submission said of the 1989 Smooth Tests of Goodness of Fit published by Oxford University Press: the seminal work by Rayner and Best on smooth goodness-of-fit tests (reflected in their monograph as well as numerous joint papers) basically reinvigorated and redefined the previously comatose area of goodness-of-fit. I am currently preparing a second edition of this book. Some 1200 copies of the first edition have been sold. The main contribution is an optimal method of statistical model assessment that can be applied to virtually any statistical model. It provides a method for deriving new tests of fit, and a standard against which any new procedure should be compared. It has been the springboard for much new research. I was invited to give a plenary presentation to an international workshop on goodness of fit in Paris in May 2000. I have also accepted invitations to write review articles in this, and related areas, for the Encyclopedia of Statistical Sciences and the International Encyclopedia of Social and Behavioral Sciences. In nonparametric statistics with John Best I have co-authored two books, A Contingency Table Approach to Nonparametric Testing, and Nonparametrics for Sensory Science: A More Informative Approach. We have also written over 30 articles for refereed journals, book chapters, conference proceedings and encyclopedias. We have pioneered a generic approach that generates penetrating new nonparametric data analysis techniques. For experimental designs where there are known nonparametric tests, the approach generates extensions of these tests. For designs where previously there were no nonparametric tests, the approach generates a suite of tests that give a detailed and informative scrutiny of the data. An invited joint presentation (with John Best) on some of this material was given to the NSW Branch of the Statistical Society of Australia in July 1999. I gave an invited plenary address to the New Zealand Mathematics Colloquium at Massey University in December 2001. I was for ten years the Statistics Editor of the Journal of Applied Mathematics and Decision Sciences, and am currently a member of their editorial board, as I am for the Journal of Statistical Theory and Practice. I have served on the International Organizing or Advisory Committees for six International Conferences on Statistics, Combinatorics and Related Areas between 2001 and 2006. These were held at Wollongong (I was one of the editors of the Proceedings of this conference), Allahabad, India, Southern Maine, USA, Lucknow, India, Auburn, Alabama, USA and at Lisbon in 2006.

Teaching Expertise
I have extensive experience that includes: " nearly four decades of lecturing the full gamut of statistics courses - service and mainstream courses, large and small classes, remedial to postgraduate students; " marking Higher School Certificate examinations in both Australia and New Zealand, and Moderator of the New Zealand Higher School Certificate Bursaries Mathematics with Statistics paper 1990 and 1991; and " publishing advice on statistical and mathematical education at a variety of levels. I have written several articles about learning statistics. They demonstrate that I have been thinking and writing about student learning for some time, and doing so at a level that is of considerable interest to my peers. My first published book was advice to Higher School Certificate students in New Zealand on project writing. At that time, in the late 1980s, project work contributed 20% to the assessment of the New Zealand Bursaries paper Mathematics with Statistics. Over 3,000 copies were sold. I wrote a parallel book for honours and thesis students. That book has been used at Otago University since I wrote it, and at Wollongong University since my arrival there in 1992. In 2000 I made this material available over the web (http://www.math.uow.edu.au/students/current/writing_02.pdf). I was Education Officer of the New Zealand Statistical Association (1987-1990) and was Secretary of the Local Organising Committee for the International Conference on Teaching Statistics (ICOTS 3) Dunedin, New Zealand, August 1990. This event was attended by over 600 mainly international delegates. I initiated and have jointly edited a special Statistical Education edition of the Journal of Applied Mathematics and Decision Sciences that appeared in 2003. My experience and focus on student learning enabled me to promote an environment of quality student learning during my two headships at the University of Wollongong. For individuals I did this in a variety of ways, including a peer mentoring scheme, individual counselling, a local workshop I organised that focused on the School's Award Winning Teachers, and following its success, a similar Inspiring Teaching workshop I organised for the NSW Branch of the Australian Statistical Society. During my headship of the School of Mathematics and Applied Statistics, three staff won teaching awards, two at Faculty level and one at national level.

Administrative Expertise
At the University of Wollongong I successfully headed both the Department of Applied Statistics and the School of Mathematics and Applied Statistics, both for three years from their difficult beginnings. In the former I oversaw a period of steady growth of student numbers and in the research achievement of my colleagues. When the Departments of Applied Statistics and Mathematics were combined into the School of Mathematics and Applied Statistics I was appointed foundation Head, with the brief that the new School had to shed seven staff. Ultimately four of 20 plus academic positions were lost as opportunities were found to service growth areas to replace previously serviced areas in decline. This was done while maintaining morale and enabling staff to remain focused on producing quality outcomes in both research and teaching. Since joining the University of Newcastle I have been head of the discipline of Statistics. During 2003 I was the Director of the Statistical Consulting Service at the University of Wollongong. Since joining the University of Newcastle I successfully lobbied for new funding for the Statistical Support Service. The Service has been reorganised and revitalised. Demonstrably I have positively influenced the research culture of my statistics colleagues. At the University of Wollongong in 2001 I was Coordinator of the Data Interpretation and Financial Analysis Program, one of five programs within the Institute of Mathematical Modelling and Computer Systems, and later Director of the Institute in 2002 and 2003. I was Chair of the Faculty of Informatics Faculty Research Committee during autumn session 2002. Since joining the University of Newcastle I have served on the Leaders and Deputies Committee of the ARC Centre for Complex Dynamic Systems and Control. In March 2002 I gave a well-received presentation On Building an Academic Research Profile (see http://www.math.uow.edu.au/research/docs/rprofile.pdf). This was attended by over 40 academics and researchers from across the University. I have served on the Council of the NSW Branch of the Statistical Society of Australia for a decade from 1995. From March 2002 to March 2004 I was President of the Branch, the biggest and arguably the most important branch of the Society. As a consequence of my presidency the branch adopted better financial practices and took on new initiatives in providing services to members. For example, one initiative was to replace the awarding of prizes and scholarships, at a considerable and variable recurrent cost, with a Postgraduate Awards event. In this event research students from each university in the state make 20 minute presentations on their research, for cash and other prizes. Since 2003 this has been a sponsored event and run at a profit to the Branch. I was an external reviewer for the Faculty of Science at the Queensland University of Technology for a new undergraduate course, the Bachelor of Mathematics, and an international reviewer for the National Science Foundation of USA in 2005.


Qualifications

  • PhD, University of Wollongong
  • Bachelor of Arts (Honours), University of Sydney
  • Master of Arts (Honours), University of Sydney

Keywords

  • goodness of fit
  • nonparametric statistics

Fields of Research

Code Description Percentage
010499 Statistics not elsewhere classified 70
080299 Computation Theory and Mathematics not elsewhere classified 10
140399 Econometrics not elsewhere classified 20

Professional Experience

Academic appointment

Dates Title Organisation / Department
1/06/2006 -  Professor of Statistics University of Newcastle
School of Mathematical and Physical Sciences
Australia
1/06/1996 - 1/02/2006 Associate Professor University of Wollongong
School of Mathematics and Applied Statistics
Australia
1/06/1992 - 1/01/1996 Senior Lecturer University of Wollongong
School of Mathematics and Applied Statistics
Australia

Membership

Dates Title Organisation / Department
Member - Journal of Statistical Theory and Practice Journal of Statistical Theory and Practice
Australia
1/03/2002 - 1/03/2004 President - N.S.W. Branch of the Statistical Society of Australia Statistical Society of Australia Inc.
Australia
1/01/2001 - 31/12/2006 Council Member - N.S.W. Branch of the Statistical Society of Australia Statistical Society of Australia Inc.
Australia
1/01/1998 - 31/12/2006 Statistics Area Editor - Journal Applied Mathematics and Decision Sciences Journal Applied Mathematics and Decision Sciences
Australia

Invitations

External Reviewer - Programs

Year Title / Rationale
2007 Faculty of Science at the Queensland University of Technology
Organisation: Queensland University of Technology Description: External reviewer for the Faculty of Science at the Queensland University of Technology for a new undergraduate course: Bachelor of Mathematics.

Participant

Year Title / Rationale
2001 Invited plenary speaker
Organisation: New Zealand Mathematics Colloquium Description: Title: Lessons from a Quarter Century of Research; Venue: Massey University, Palmerston North, New Zealand; Date: December 3-6, 2001;
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (5 outputs)

Year Citation Altmetrics Link
2009 Rayner JC, Thas O, Best DJ, Smooth Tests of Goodness of Fit: Using R, John Wiley & Sons (Asia), Singapore, 272 (2009) [A3]
Co-authors John Best
2008 Rayner JCW, Best DJ, Brockhoff PB, Rayner GD, Nonparametrics for Sensory Science: A More Informative Approach (2008) [A1]

Sensory evaluation is the perception science of the food industry. Sensory data can be costly to obtain and so gleaning the most information possible from the data is key. Increas... [more]

Sensory evaluation is the perception science of the food industry. Sensory data can be costly to obtain and so gleaning the most information possible from the data is key. Increasingly, value is added to sensory evaluation by the use of statistics, especially to improve the quality of product development and to make the most of market research. Nonparametrics for Sensory Science is written to complement existing parametric methodology. Nonparametric methods are appropriate when facts are only available in nominal or ordinal form, and when the model assumptions necessary for parametric procedures do not hold. Author Rayner and his colleagues consider problems including the most commonly occurring and important experimental designs: the one-sample, k-sample, blocked samples, samples with factorial structure and samples with correlation structure. Innovative new techniques are outlined and complemented with real examples. Techniques described may be applied to data where the traditional, most frequently applied nonparametric tests, such as the Kruskal-Wallis, the Friedman and the Spearman tests, are applied. Those familiar with traditional nonparametric testing will be able to update their knowledge, acquiring powerful new methods. Those without prior knowledge of nonparametric testing will be able to acquire that knowledge through this book. Aimed at sensory scientists and statisticians interested in nonparametrics, the techniques of Nonparametrics for Sensory Science are of broad general interest, but are of particular interest in sensory evaluation applications. © 2005 John Charles Rayner, John Best, Per Brunn Brockhoff, and Glen Rayner.

DOI 10.1002/9780470752586
Citations Scopus - 8
2005 Beh EJ, Clark RG, Rayner, Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong Press, University of Wollongong, 185 (2005)
Co-authors Eric Beh
2005 Beh EJ, Clark RG, Rayner, Proceedings of the 2004 Workshop on Research Methods: Statistics and Finance, University of Wollongong Press, University of Wollongong, 185 (2005)
Co-authors Eric Beh
2001 Rayner JCW, Best DJ, A Contingency Table Approach to Nonparametric Testing., Chapman & Hall/CRC, 256 (2001) [A1]
Show 2 more books

Chapter (9 outputs)

Year Citation Altmetrics Link
2015 Rayner JCW, Suesse TF, Thas O, 'Smooth Tests of Fit for Gaussian Mixtures', Data Science, Learning by Latent Structures, and Knowledge Discovery, Springer, Heidelberg 133-142 (2015)
DOI 10.1007/978-3-662-44983-7_12
2003 Rayner JCW, 'Extended analysis for ranked data with ties', Lecture notes in statistics; an easy learning approach, Modelling and Simulation Research, Penrith, NSW, Australia 193-201 (2003) [B2]
2003 Rayner JCW, 'More informative new nonparametric testing for important experimental designs', Lecture notes in statistics; an easy learning approach, Modelling and Simulation Research, Penrith, NSW, Australia 157-171 (2003) [B2]
2003 Rayner JCW, 'Generalised correlations and Simpson''s paradox', Lecture notes in statistics; an easy learning approach, Modelling and Simulation Research, Penrith, NSW, Australia 63-73 (2003) [B2]
2002 Rayner JCW, 'Partially Parametric Testing', , Birkhauser, Boston, 423-431 (2002) [B1]
2002 Rayner JCW, 'Using Contingency Tables to Construct both Traditional and New Nonparametric Tests.', , World Scientific Press, Singapore, 247-257 (2002) [B1]
2002 Rayner JCW, 'Chisquared Components as Tests of Fit for Discrete Distributions', , World Scientific Press, Singapore, 23-31 (2002) [B1]
2002 Rayner JCW, 'Testing Equality of Corresponding Variances from Multiple Covariance Matrices', , World Scientific Press, Singapore, 157-166 (2002) [B1]
2001 Rayner JCW, 'Goodness-of-fit tests and diagnostics', , Elsevier, Adelaide, 6305-6310 (2001) [B1]
Show 6 more chapters

Journal article (117 outputs)

Year Citation Altmetrics Link
2017 Best DJ, Rayner JCW, 'A note on additional statistical analysis for JAR data', FOOD QUALITY AND PREFERENCE, 55 6-7 (2017)
DOI 10.1016/j.foodqual.2016.08.005
2016 Best DJ, Rayner JCW, Thas O, De Neve J, Allingham D, 'Comparing Nonparametric Tests of Equality of Means for Randomized Block Designs', Communications in Statistics: Simulation and Computation, 45 1718-1730 (2016) [C1]

Copyright © Taylor & Francis Group, LLC.A number of nonparametric tests are compared empirically for a randomized block layout. We assess tests appropriate for when the data are ... [more]

Copyright © Taylor & Francis Group, LLC.A number of nonparametric tests are compared empirically for a randomized block layout. We assess tests appropriate for when the data are not consistent with normality or when outliers invalidate traditional analysis of variance (ANOVA) tests. The objective is to assess, within this setting, tests that use ranks within blocks, the rank transform procedure that ranks the complete sample and continuous analogs of the Cochran-Mantel-Haenszel tests. The usual linear model is assumed, and our primary foci are tests of equality of means and component tests that assess linear and quadratic trends in the means. These tests include the traditional Page and Friedman tests. We conclude that the rank transform tests have competitive power and warrant greater use than is currently apparent.

DOI 10.1080/03610918.2013.861483
Co-authors John Best
2016 Best DJ, Rayner JCW, 'Analysis of ranked data in randomized blocks when there are missing values', Journal of Applied Statistics, 1-8 (2016)

© 2016 Taylor & FrancisData consisting of ranks within blocks are considered for randomized block designs when there are missing values. Tied ranks are possible. Such data can be... [more]

© 2016 Taylor & FrancisData consisting of ranks within blocks are considered for randomized block designs when there are missing values. Tied ranks are possible. Such data can be analysed using the Skillings¿Mack test. Here we suggest a new approach based on carrying out an ANOVA on the ranks using the general linear model platform available in many statistical packages. Such a platform allows an ANOVA to be calculated when there are missing values. Indicative sizes and powers show the ANOVA approach performs better than the Skillings¿Mack test.

DOI 10.1080/02664763.2016.1158245
Co-authors John Best
2016 Best DJ, Rayner JCW, Thas O, 'Corrigendum to ¿Comparison of Some Tests of Fit for the Inverse Gaussian Distribution¿', Advances in Decision Sciences, 2016 1-2 (2016)
DOI 10.1155/2016/1097157
2015 Thas O, Rayner JCW, De Neve J, 'GENERALISED SMOOTH TESTS OF GOODNESS OF FIT UTILISING L-MOMENTS', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 57 481-499 (2015) [C1]
DOI 10.1111/anzs.12130
2015 Rayner JCW, Best DJ, Thas O, 'Extended Analysis of At Least Partially Ordered Multi-factor ANOVA', Australian and New Zealand Journal of Statistics, 57 211-224 (2015) [C1]

© 2015 Australian Statistical Publishing Association Inc.For multifactor experimental designs in which the levels of at least one of the factors are ordered we show how to constr... [more]

© 2015 Australian Statistical Publishing Association Inc.For multifactor experimental designs in which the levels of at least one of the factors are ordered we show how to construct components that provide a deep nonparametric scrutiny of the data. The components assess generalised correlations and the resulting tests include and extend the Page and umbrella tests. Application of the tests described is straightforward. Orthonormal polynomials on the ANOVA responses and the factors are required and the formulae needed are given subsequently. These depend on the moments of the responses and of each factor and are easily calculated. Products of at least two of these orthonormal polynomials are then used as inputs into standard ANOVA routines. For example, using the first order orthonormal polynomial on factor A and the second order orthonormal polynomial on the ANOVA response will assess if, with increasing levels of factor A there is an umbrella response with either an increase and then a decrease or a decrease and then an increase.

DOI 10.1111/anzs.12113
Co-authors John Best
2015 Rayner JCW, SUESSE TF, THAS O, 'Smooth tests of fit for Gaussian mixtures', Studies in Classification, Data Analysis and Knowledge Organisation, 133-142 (2015) [C1]
DOI 10.1007/978-3-662-44983-7_12
2015 Best DJ, Rayner JCW, 'An alternative to pages test permitting both tied and missing data', Journal of Statistical Theory and Practice, 9 524-536 (2015) [C1]

© Grace Scientific Publishing, LLC.Data consisting of ranks within blocks are considered for randomized complete block layouts where treatment effects are expected to be ordered.... [more]

© Grace Scientific Publishing, LLC.Data consisting of ranks within blocks are considered for randomized complete block layouts where treatment effects are expected to be ordered. Ranks with and without ties are considered, as well as missing values. A small indicative test size study indicates both a new test and the Page test, modified by Thas et al. (2012) to easily permit ties, perform well. An advantage of the new test is that it can be easily applied to data with missing values. Three real examples are given. One of these illustrates a quadratic trend test. Comparisons between the new test and the Alvo and Cabilio (1995) extended Page test for missing values are given.

DOI 10.1080/15598608.2014.940098
Co-authors John Best
2014 Best DJ, Rayner JCW, 'Conover's F test as an alternative to durbin's test', Journal of Modern Applied Statistical Methods, 13 76-83 (2014) [C1]

© 2014 JMASM, Inc.Data consisting of ranks within blocks are considered for balanced incomplete block designs. An F test statistic from ANOVA is better approximated by an F distr... [more]

© 2014 JMASM, Inc.Data consisting of ranks within blocks are considered for balanced incomplete block designs. An F test statistic from ANOVA is better approximated by an F distribution than the Durbin statistic is approximated by a chi-squared distribution. Indicative powers demonstrate that the F test is generally superior to Durbin's test.

Co-authors John Best
2014 Best DJ, Rayner JCW, Allingham D, 'A note on formulae for CMH statistics for JAR data', Food Quality and Preference, 31 19-21 (2014) [C1]

Cochran-Mantel-Haenszel (CMH) test statistics can be used to compare products rated on JAR 'just about right' scales and for similar categorical data. In this note we consider the... [more]

Cochran-Mantel-Haenszel (CMH) test statistics can be used to compare products rated on JAR 'just about right' scales and for similar categorical data. In this note we consider the case of paired or related data. The simplified statistics we give allow 'by hand' calculation when the data set is small. We also give an R package for larger data sets or for when the user is not interested in 'by hand' calculation. © 2013 Elsevier Ltd.

DOI 10.1016/j.foodqual.2013.07.006
Citations Scopus - 1Web of Science - 1
Co-authors John Best
2013 Rayner JCW, Thas O, Pipelers P, Beh EJ, 'Calculating bivariate orthonormal polynomials by recurrence', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 55 15-24 (2013) [C1]
DOI 10.1111/anzs.12011
Citations Scopus - 1Web of Science - 1
Co-authors Eric Beh
2013 Rayner JCW, Best DJ, 'Extended Anova And Rank Transform Procedures', Australian & New Zealand Journal Of Statistics, 55 305-319 (2013) [C1]
DOI 10.1111/anzs.12041
Citations Scopus - 3Web of Science - 2
Co-authors John Best
2012 Thas O, Clement L, Rayner JC, Carvalho B, Van Criekinge W, 'An omnibus consistent adaptive percentile modified Wilcoxon rank sum test with applications in gene expression studies', Biometrics, 68 446-454 (2012) [C1]
Citations Scopus - 3Web of Science - 3
2012 Thas O, Best DJ, Rayner JC, 'Using orthogonal trend contrasts for testing ranked data with ordered alternatives', Statistica Neerlandica, 66 452-471 (2012) [C1]
DOI 10.1111/j.1467-9574.2012.00525.x
Citations Scopus - 1
Co-authors John Best
2012 Allingham D, Rayner JC, 'Testing equality of variances for multiple univariate normal populations', Journal of Statistical Theory and Practice, 6 524-535 (2012) [C1]
2012 Best DJ, Rayner JC, Thas O, 'Comparison of some tests of fit for the inverse Gaussian distribution', Advances in Decision Sciences, 2012 150303 (2012) [C1]
Citations Scopus - 1
Co-authors John Best
2011 De Boeck B, Thas O, Rayner JC, Best DJ, 'Generalised smooth tests for the generalised Pareto distribution', Journal of Statistical Theory and Practice, 5 737-750 (2011) [C1]
DOI 10.1080/15598608.2011.10483742
Citations Scopus - 1
Co-authors John Best
2011 Rayner JC, Thas O, Best DJ, 'Smooth tests of goodness of fit', Wiley Interdisciplinary Reviews: Computational Statistics, 3 397-406 (2011) [C1]
Co-authors John Best
2011 Allingham D, Rayner JC, 'A nonparametric two-sample wald test of equality of variances', Advances in Decision Sciences, 2011 748580 (2011) [C1]
Citations Scopus - 2
2011 De Boeck B, Thas O, Rayner JC, Best DJ, 'Smooth tests for the gamma distribution', Journal of Statistical Computation and Simulation, 81 843-855 (2011) [C1]
DOI 10.1080/00949650903520936
Citations Scopus - 3Web of Science - 2
Co-authors John Best
2011 Best DJ, Rayner JC, Allingham D, 'A statistical test for ranking data from partially balanced incomplete block designs', Journal of Sensory Studies, 26 81-84 (2011) [C1]
DOI 10.1111/j.1745-459X.2010.00324.x
Citations Scopus - 2Web of Science - 1
Co-authors John Best
2011 Best DJ, Rayner JC, Thas O, 'Easily appled tests of fit for the Rayleigh distribution', Sankhya B - Applied and Interdisciplinary Statistics, 72 254-263 (2011) [C1]
Citations Scopus - 4
Co-authors John Best
2010 Rippon PG, Rayner JC, 'Generalised score and Wald tests', Advances in Decision Sciences, 2010 Article ID 292013 (2010) [C1]
DOI 10.1155/2010/292013
Citations Scopus - 3
Co-authors Paul Rippon
2010 Rayner JCW, Thas O, Best DJ, 'Smooth Tests of Goodness of Fit: Using R: Second Edition', Smooth Tests of Goodness of Fit: Using R: Second Edition, (2010)

In this fully revised and expanded edition of Smooth Tests of Goodness of Fit, the latest powerful techniques for assessing statistical and probabilistic models using this proven ... [more]

In this fully revised and expanded edition of Smooth Tests of Goodness of Fit, the latest powerful techniques for assessing statistical and probabilistic models using this proven class of procedures are presented in a practical and easily accessible manner. Emphasis is placed on modern developments such as data-driven tests, diagnostic properties, and model selection techniques. Applicable to most statistical distributions, the methodology described in this book is optimal for deriving tests of fit for new distributions and complex probabilistic models, and is a standard against which new procedures should be compared. New features of the second edition include: Expansion of the methodology to cover virtually any statistical distribution, including exponential families. Discussion and application of data-driven smooth tests. Techniques for the selection of the best model for the data, with a guide to acceptable alternatives. Numerous new, revised, and expanded examples, generated using R code. Smooth Tests of Goodness of Fit is an invaluable resource for all methodological researchers as well as graduate students undertaking goodness-of-fit, statistical, and probabilistic model assessment courses. Practitioners wishing to make an informed choice of goodness-of-fit test will also find this book an indispensible guide. Reviews of the first edition: "This book gives a very readable account of the smooth tests of goodness of fit. The book can be read by scientists having only an introductory knowledge of statistics. It contains a fairly extensive list of references; research will find it helpful for the further development of smooth tests." --T.K. Chandra, Zentralblatt für Mathematik und ihre Grenzgebiete, Band 73, 1/92' "An excellent job of showing how smooth tests (a class of goodness of fit tests) are generally and easily applicable in assessing the validity of models involving statistical distributions....Highly recommended for undergraduate and graduate libraries." --Choice. "The book can be read by scientists having only an introductory knowledge of statistics. It contains a fairly extensive list of references; researchers will find it helpful for the further development of smooth tests."--Mathematical Reviews. "Very rich in examples . . . Should find its way to the desks of many statisticians." --Technometrics. © 2009 John Wiley & Sons (Asia) Pte Ltd.

DOI 10.1002/9780470824443
Co-authors John Best
2010 Best DJ, Rayner JC, Thas O, 'Four tests of fit for the beta-binomial distribution', Journal of Applied Statistics, 37 1547-1554 (2010) [C1]
DOI 10.1080/02664760903089664
Co-authors John Best
2010 Best DJ, Rayner JC, Thas O, 'Moment tests of fit for some discrete distributions with ecological applications', International Journal of Ecological Economics and Statistics, 17 1-15 (2010) [C1]
Co-authors John Best
2009 Best DJ, Rayner JC, Thas O, 'Anscombe's Tests of fit for the negative binomial distribution', Journal of Statistical Theory and Practice, 3 555-565 (2009) [C1]
DOI 10.1080/15598608.2009.10411946
Co-authors John Best
2009 Rayner JC, Carolan AM, 'Partially parametric testing', Journal of Statistical Theory and Practice, 3 735-750 (2009) [C1]
DOI 10.1080/15598608.2009.10411956
2009 Rayner JC, Best DJ, Thas O, 'Generalised smooth tests of goodness of fit', Journal of Statistical Theory and Practice, 3 665-679 (2009) [C1]
DOI 10.1080/15598608.2009.10411953
Co-authors John Best
2009 Thas O, Rayner JC, Best DJ, De Boeck D, 'Informative statistical analyses using smooth goodness of fit tests', Journal of Statistical Theory and Practice, 3 705-733 (2009) [C1]
DOI 10.1080/15598608.2009.10411955
Co-authors John Best
2009 Rayner JC, Best DJ, Thas O, 'Guest editors', Journal of Statistical Theory and Practice, 3 (2009) [C2]
Co-authors John Best
2009 Rayner JC, Thas O, Best DJ, 'Introduction to modern goodness of fit methods', Journal of Statistical Theory and Practice, 3 537-541 (2009) [C3]
DOI 10.1080/15598608.2009.10411944
Co-authors John Best
2009 Rayner JC, Beh EJ, 'Towards a better understanding of correlation', Statistica Neerlandica, 63 324-333 (2009) [C1]
DOI 10.1111/j.1467-9574.2009.00425.x
Citations Scopus - 5Web of Science - 7
Co-authors Eric Beh
2009 Rayner JC, Beh EJ, 'Components of Pearson's statistic for at least partially ordered m-way contingency tables', Journal of Applied Mathematics and Decision Sciences, 2009 1-9 (2009) [C1]
DOI 10.1155/2009/980706
Citations Scopus - 4
Co-authors Eric Beh
2008 Rayner JC, Thas O, De Boeck B, 'A generalised Emerson recurrence relation', Australian and New Zealand Journal of Statistics, 50 235-240 (2008) [C1]
DOI 10.1111/j.1467-842x.2008.00514.x
Citations Scopus - 9Web of Science - 5
2008 Best DJ, Rayner JC, Thas O, 'Tests of fit for the logarithmic distribution', Journal of Applied Mathematics and Decision Sciences, 2008 463781 (2008) [C1]
DOI 10.1155/2008/463781
Citations Scopus - 1
Co-authors John Best
2008 Best DJ, Rayner JC, Thas O, 'Comparison of some tests of fit for the Laplace distribution', Computational Statistics and Data Analysis, 52 5338-5343 (2008) [C1]
DOI 10.1016/j.csda.2008.05.023
Citations Scopus - 4Web of Science - 2
Co-authors John Best
2008 Best DJ, Rayner JC, Thas O, 'X-2 and its components as tests of normality for grouped data', Journal of Applied Statistics, 35 481-492 (2008) [C1]
DOI 10.1080/02664760701835219
Citations Scopus - 2Web of Science - 1
Co-authors John Best
2007 Best DJ, Rayner JC, Thas O, 'Comparison of five tests of fit for the extreme value distribution', Journal of Statistical Theory and Practice, 1 89-99 (2007) [C1]
Co-authors John Best
2007 Best DJ, Rayner JC, Thas O, 'Goodness of fit for the zero-truncated Poisson distribution', Journal of Statistical Computation and Simulation, 77 585-591 (2007) [C1]
DOI 10.1080/10629360600569329
Citations Scopus - 4Web of Science - 2
Co-authors John Best
2007 Best DJ, Rayner JC, 'Chi-squared components for tests of fit and improved models for the grouped exponential distribution', Computational Statistics and Data Analysis, 51 3946-3954 (2007) [C1]
DOI 10.1016/j.csda.2006.03.014
Citations Scopus - 5Web of Science - 4
Co-authors John Best
2006 Best DJ, Brockhoff PB, Rayner JCW, 'Tests for balanced incomplete block ranked data with ties', STATISTICA NEERLANDICA, 60 3-11 (2006) [C1]
DOI 10.1111/j.1467-9574.2006.00305.x
Citations Scopus - 2Web of Science - 2
2006 Best DJ, Rayner JCW, 'Improved testing for the binomial distribution using chi-squared components with data-dependent cells', JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 76 75-81 (2006) [C1]
DOI 10.1080/00949650412331320891
Citations Scopus - 3Web of Science - 2
2006 Thas O, Best DJ, Rayner JC, 'Nonparametric analysis of blocked ordered categories data: some examples revisited', Journal of Applied Mathematics and Decision Sciences, 2006 - (2006) [C1]
DOI 10.1155/JAMDS/2006/31089
Co-authors John Best
2005 Thas O, Rayner JCW, 'Smooth tests for the zero-inflated poisson distribution', BIOMETRICS, 61 808-815 (2005) [C1]
DOI 10.1111/j.1541-0420.2005.00351.x
Citations Scopus - 17Web of Science - 11
2005 Best DJ, Rayner JCW, 'Improved testing for the Poisson distribution using chisquared components with data dependent cells', COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 34 85-96 (2005) [C1]
DOI 10.1081/SAC-200053153
Citations Scopus - 2Web of Science - 2
2005 Thas O, Rayner JCW, Best DJ, 'Tests for symmetry based on the one-sample Wilcoxon signed rank statistic', COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 34 957-973 (2005) [C1]
DOI 10.1080/03610910500308354
Citations Scopus - 10Web of Science - 9
2005 Rayner JCW, Thas O, 'More informative testing for bivariate symmetry', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 47 211-217 (2005) [C1]
DOI 10.1111/j.1467-842X.2005.00385.x
Citations Scopus - 1Web of Science - 1
2004 Brockhoff PB, Best DJ, Rayner JCW, 'Partitioning Anderson's statistic for tied data', JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 121 93-111 (2004) [C1]
DOI 10.1016/S0378-3758(02)00508-6
Citations Scopus - 6Web of Science - 4
2004 Brockhoff PB, Best DJ, Rayner JCW, 'An application of extended analysis for ranked data with ties', AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 46 197-204 (2004) [C1]
DOI 10.1111/j.1467-842X.2004.00324.x
2003 Best DJ, Rayner JCW, 'Tests of fit for the geometric distribution', COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 32 1065-1078 (2003) [C1]
DOI 10.1081/SAC-120023878
Citations Scopus - 7Web of Science - 7
2003 Brockhoff PB, Best DJ, Rayner JCW, 'Using Anderson's statistic to compare distributions of consumer preference rankings', JOURNAL OF SENSORY STUDIES, 18 77-82 (2003)
DOI 10.1111/j.1745-459X.2003.tb00374.x
Citations Scopus - 3Web of Science - 2
2001 Rayner GD, Rayner JCW, 'Power of the Neyman smooth tests for the uniform distribution', Journal of Applied Mathematics and Decision Sciences, 5 181-191 (2001) [C1]

This paper compares and investigates the generalised Neyman smooth test, its components, and the classical chi-squared test with a variety of equiprobable classes. Each test is ev... [more]

This paper compares and investigates the generalised Neyman smooth test, its components, and the classical chi-squared test with a variety of equiprobable classes. Each test is evaluated in terms of its power to reject a wavelike alternative to the uniform distribution, chosen to quantify the complexity of the alternative. Results indicate that if broadly focused tests (rather than strongly directional or weakly omnibus) are sought, then smooth tests of order about four, or the chi-squared test with between five and ten classes, will perform well. Copyright© 2001, Lawrence Erlbaum Associates, Inc.

Citations Scopus - 6
2001 Carolan AM, Rayner JCW, 'One sample tests for the location of modes of nonnormal data', Journal of Applied Mathematics and Decision Sciences, 5 1-19 (2001) [C1]

There are few techniques available for testing if modes take specified values. We show that standard tests of location such as the t-test and the Wilcoxon test, which test for the... [more]

There are few techniques available for testing if modes take specified values. We show that standard tests of location such as the t-test and the Wilcoxon test, which test for the mean and median respectively, can perform poorly as tests for modes when the data is other than unimodal and symmetric. Carolan and Rayner [1] proposed a score test of location for symmetric nonnormal data. We consider a family of distributions similar to those considered by Carolan and Rayner [1] and propose a test for the mode or modes of data from multimodal or skewed distributions and demonstrate by way of simulations that it is reasonably effective. Copyright© 2001, Lawrence Erlbaum Associates, Inc.

Citations Scopus - 1
2001 Best DJ, Rayner JCW, 'Nonparametric analysis for trinary sensory data', JOURNAL OF SENSORY STUDIES, 16 249-260 (2001)
DOI 10.1111/j.1745-459X.2001.tb00299.x
Citations Scopus - 1Web of Science - 1
2001 Best DJ, Rayner J, 'Application of the Stuart test to sensory evaluation data', Food Quality and Preference, 12 353-357 (2001) [C1]
2000 Carolan AM, Rayner JCW, 'Wald tests of location for symmetric nonnormal data', BIOMETRICAL JOURNAL, 42 777-792 (2000)
2000 Carolan AM, Rayner JCW, 'One sample tests of location for nonnormal symmetric data', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 29 1569-1581 (2000)
DOI 10.1080/03610920008832565
Citations Scopus - 3Web of Science - 2
2000 Jones G, Lai CD, Rayner JCW, 'A bivariate gamma mixture distribution', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 29 2775-2790 (2000)
DOI 10.1080/03610920008832636
Citations Scopus - 3Web of Science - 2
2000 Best DJ, Rayner JCW, 'Extended statistical analysis of ranked data from balanced incomplete block and paired comparison designs', JOURNAL OF SENSORY STUDIES, 15 383-392 (2000)
DOI 10.1111/j.1745-459X.2000.tb00277.x
Citations Scopus - 2Web of Science - 2
2000 Rayner JCW, Best DJ, 'Analysis of singly ordered two-way contingency tables', Journal of Applied Mathematics and Decision Sciences, 4 83-98 (2000)

Pearson's statistic is investigated for nominal-ordinal two-way contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the first summ... [more]

Pearson's statistic is investigated for nominal-ordinal two-way contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the first summand of which is a statistic given by Yates (1948), and examines location effects for the nominal category. The second and subsequent summands reflect the corresponding moments: for example, dispersion, skewness, kurtosis etc. The summands are shown to be weakly optimal in that they are score statistics. © Journal of Applied Mathematics & Decision Sciences.

Citations Scopus - 9
1999 Rayner JCW, 'Modelling ties in the sign test', BIOMETRICS, 55 663-665 (1999)
DOI 10.1111/j.0006-341X.1999.00663.x
Citations Scopus - 13Web of Science - 12
1999 Lai CD, Rayner JCW, Hutchinson TP, 'Robustness of the sample correlation - The bivariate lognormal case', Journal of Applied Mathematics and Decision Sciences, 3 7-19 (1999)

The sample correlation coefficient R is almost universally used to estimate the population correlation coefficient p. If the pair (X, Y) has a bivariate normal distribution, this ... [more]

The sample correlation coefficient R is almost universally used to estimate the population correlation coefficient p. If the pair (X, Y) has a bivariate normal distribution, this would not cause any trouble. However, if the marginals are nonnormal, particularly if they have high skewness and kurtosis, the estimated value from a sample may be quite different from the population correlation coefficient ¿. The bivariate lognormal is chosen as our case study for this robustness study. Two approaches are used: (i) by simulation and (ii) numerical computations. Our simulation analysis indicates that for the bivariate lognormal, the bias in estimating p¿ can be very large if ¿ ¿0, and it can be substantially reduced only after a large number (three to four million) of observations. This phenomenon, though unexpected at first, was found to be consistent to our findings by our numerical analysis. © Journal of Applied Mathematics & Decision Sciences.

Citations Scopus - 13
1999 Rayner JCW, Best DJ, 'Nonparametric tests for data in randomised blocks with ordered alternatives', Journal of Applied Mathematics and Decision Sciences, 3 143-153 (1999)

For randomized block designs, nonparametric treatment comparisons are usually made using the Friedman test for complete designs, and the Durbin test for incomplete designs; see, f... [more]

For randomized block designs, nonparametric treatment comparisons are usually made using the Friedman test for complete designs, and the Durbin test for incomplete designs; see, for example, Conover (1998). This permits assessment of only the mean rankings. Such comparisons are here extended to permit assessments of bivariate effects such as the linear by linear effect and the quadratic by linear, or umbrella effect. © Journal of Applied Mathematics & Decision Sciences.

Citations Scopus - 1
1999 Best DJ, Rayner JCW, 'Goodness of fit for the Poisson distribution', STATISTICS & PROBABILITY LETTERS, 44 259-265 (1999)
DOI 10.1016/S0167-7152(99)00017-6
Citations Scopus - 5Web of Science - 7
1998 Best DJ, Rayner JCW, 'Nonparametric analysis of ordinal categorical response data with factorial structure', JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS, 47 439-446 (1998)
Citations Web of Science - 7
1998 Best DJ, Rayner JCW, Stephens LG, 'Small-sample comparison of McCullagh and Nair analyses for nominal-ordinal categorical data', COMPUTATIONAL STATISTICS & DATA ANALYSIS, 28 217-223 (1998)
DOI 10.1016/S0167-9473(98)00031-0
Citations Scopus - 5Web of Science - 3
1998 Rayner JCW, Rayner GD, 'S-sample smooth goodness of fit testing: Rederivation and Monte Carlo assessment', BIOMETRICAL JOURNAL, 40 651-663 (1998)
1997 Best DJ, Rayner JCW, 'Goodness of fit for the binomial distribution', AUSTRALIAN JOURNAL OF STATISTICS, 39 355-364 (1997)
Citations Web of Science - 3
1997 Rayner JCW, 'The asymptotically optimal tests', STATISTICIAN, 46 337-346 (1997)
Citations Scopus - 13Web of Science - 5
1997 Best DJ, Rayner JCW, 'Product maps for ranked preference data', STATISTICIAN, 46 347-354 (1997)
Citations Scopus - 2Web of Science - 1
1997 Rayner JCW, Best DJ, 'How order affects the sign test', BIOMETRICS, 53 1416-1421 (1997)
DOI 10.2307/2533507
1997 Rayner JCW, Best DJ, 'Extensions to the Kruskal-Wallis test and a generalised median test with extensions', Journal of Applied Mathematics and Decision Sciences, 1 13-25 (1997)

The data for the tests considered here may be presented in two-way contingency tables with all marginal totals fixed. We show that Pearson's test statistic XP2 (P for Pearson) may... [more]

The data for the tests considered here may be presented in two-way contingency tables with all marginal totals fixed. We show that Pearson's test statistic XP2 (P for Pearson) may be partitioned into useful and informative components. The first detects location differences between the treatments, and the subsequent components detect dispersion and higher order moment differences. For Kruskal-Wallis-type data when there are no ties, the location component is the Kruskal-Wallis test. The subsequent components are the extensions. Our approach enables us to generalise to when there are ties, and to when there is a fixed number of categories and a large number of observations. We also propose a generalisation of the well-known median test. In this situation the location-detecting first component of X P2 reduces to the usual median test statistic when there are only two categories. Subsequent components detect higher moment departures from the null hypothesis of equal treatment effects. © Journal of Applied Mathematics & Decision Sciences.

Citations Scopus - 3
1997 Best DJ, Rayner JCW, 'Crockett's test of fit for the bivariate Poisson', BIOMETRICAL JOURNAL, 39 423-430 (1997)
DOI 10.1002/bimj.4710390404
Citations Scopus - 1
1997 Best DJ, Rayner JCW, 'Goodness of fit for the ordered categories discrete uniform distribution', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 26 899-909 (1997)
DOI 10.1080/03610929708831957
Citations Scopus - 2Web of Science - 2
1996 Best DJ, Rayner JCW, 'Nonparametric analysis for doubly ordered two-way contingency tables', BIOMETRICS, 52 1153-1156 (1996)
DOI 10.2307/2533077
Citations Scopus - 25Web of Science - 21
1996 Rayner JCW, Best DJ, 'Smooth extensions of Pearsons's product moment correlation and Spearman's rho', STATISTICS & PROBABILITY LETTERS, 30 171-177 (1996)
DOI 10.1016/0167-7152(95)00216-2
Citations Scopus - 20Web of Science - 16
1996 Davy PJ, Rayner JCW, 'Multivariate geometric distributions', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 25 2971-2987 (1996)
Citations Scopus - 1Web of Science - 1
1995 RAYNER JCW, BEST DJ, MATHEWS KL, 'INTERPRETING THE SKEWNESS COEFFICIENT', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 24 593-600 (1995)
DOI 10.1080/03610929508831509
Citations Scopus - 27Web of Science - 21
1995 Rayner JCW, Best DJ, 'SMOOTH TESTS FOR THE BIVARIATE POISSON DISTRIBUTION', Australian Journal of Statistics, 37 233-245 (1995)

A theorem of Rayner & Best (1989) is generalised to permit the construction of smooth tests of goodness of fit without requiring a set of orthonormal functions on the hypothesised... [more]

A theorem of Rayner & Best (1989) is generalised to permit the construction of smooth tests of goodness of fit without requiring a set of orthonormal functions on the hypothesised distribution. This result is used to construct smooth tests for the bivariate Poisson distribution. The test due to Crockett (1979) is similar to a smooth test that assesses the variance structure under the bivariate Poisson model; the test due to Loukas & Kemp (1986) is related to a smooth test that seeks to detect a particular linear relationship between the variances and covariance under the bivariate Poisson model. Using focused smooth tests may be more informative than using previously suggested tests. The distribution of the Loukas & Kemp (1986) statistic is not well approximated by the x2distribution for larger correlations, and a revised statistic is suggested. Copyright © 1995, Wiley Blackwell. All rights reserved

DOI 10.1111/j.1467-842X.1995.tb00656.x
1994 BEST DJ, GRAHAM D, RAYNER JCW, 'ESTIMATING CORRELATION FROM CATEGORIZED BIVARIATE NORMAL DATA', JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 49 141-149 (1994)
DOI 10.1080/00949659408811567
1993 Rayner JCW, 'Assumptions are Important: the Paired and Pooled t tests', Teaching Statistics, 15 15-17 (1993)

The relationship between the test statistics for the paired and pooled t tests, when applied to the same data set, is obtained. This assists us to understand why each is preferred... [more]

The relationship between the test statistics for the paired and pooled t tests, when applied to the same data set, is obtained. This assists us to understand why each is preferred over the other in appropriate circumstances. Copyright © 1993, Wiley Blackwell. All rights reserved

DOI 10.1111/j.1467-9639.1993.tb00249.x
Citations Scopus - 1
1992 Best DJ, Rayner JC, 'Response', Technometrics, 34 250 (1992)
DOI 10.1080/00401706.1992.10484948
1992 BEST DJ, RAYNER JCW, 'DISEASE CLUSTERING IN TIME - REPLY', BIOMETRICS, 48 327-327 (1992)
1992 RAYNER JCW, LIDDELL GF, SEYB AJ, 'THE EFFECT OF CATEGORIZATION ON BALANCED INCOMPLETE BLOCKS AND LATIN SQUARES', BIOMETRICAL JOURNAL, 34 37-55 (1992)
DOI 10.1002/bimj.4710340105
1991 BEST DJ, RAYNER JCW, 'DISEASE CLUSTERING IN TIME', BIOMETRICS, 47 589-593 (1991)
DOI 10.2307/2532148
Citations Web of Science - 6
1991 Rayner JCW, Best DJ, 'What Divisor for the Sample Variance?', Teaching Statistics, 13 85-87 (1991)

Simulation is used to show why the divisor in the sample variance is n, - 1. Choice of the divisor for the sample standard deviation is also discussed. Copyright © 1991, Wiley Bl... [more]

Simulation is used to show why the divisor in the sample variance is n, - 1. Choice of the divisor for the sample standard deviation is also discussed. Copyright © 1991, Wiley Blackwell. All rights reserved

DOI 10.1111/j.1467-9639.1991.tb00184.x
1991 RAYNER JCW, BEST DJ, LIDDELL GF, 'OPTIMAL TESTING IN A 3 WAY ANOVA MODEL', COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 20 411-425 (1991)
DOI 10.1080/03610919108812962
Citations Web of Science - 2
1990 RAYNER JCW, MCALEVEY LG, 'SMOOTH GOODNESS OF FIT TESTS FOR CATEGORIZED COMPOSITE NULL HYPOTHESES', STATISTICS & PROBABILITY LETTERS, 9 423-429 (1990)
DOI 10.1016/0167-7152(90)90034-5
Citations Scopus - 2Web of Science - 1
1990 RAYNER JCW, BEST DJ, 'A COMPARISON OF SOME RANK-TESTS USED IN TASTE-TESTING', JOURNAL OF THE ROYAL SOCIETY OF NEW ZEALAND, 20 269-272 (1990)
Citations Scopus - 1
1990 RAYNER JCW, BEST DJ, 'SMOOTH TESTS OF GOODNESS OF FIT - AN OVERVIEW', INTERNATIONAL STATISTICAL REVIEW, 58 9-17 (1990)
DOI 10.2307/1403470
Citations Web of Science - 36
1989 BEST DJ, RAYNER JCW, 'GOODNESS OF FIT FOR THE GEOMETRIC DISTRIBUTION', BIOMETRICAL JOURNAL, 31 307-311 (1989)
DOI 10.1002/bimj.4710310307
Citations Web of Science - 5
1989 MANLY BFJ, RAYNER JCW, 'CONSIDERATIONS FOR EFFECTIVE SIMULATION STUDY ANALYSIS - COMMENTS', COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 18 1241-1244 (1989)
DOI 10.1080/03610918908812817
1988 RAYNER JCW, 'CONSTRUCTING A USABLE OVERLAPPING CELLS X2 GOODNESS OF FIT TEST', STATISTICS & PROBABILITY LETTERS, 6 257-261 (1988)
DOI 10.1016/0167-7152(88)90071-5
Citations Scopus - 1
1988 BEST DJ, RAYNER JCW, 'A TEST FOR BIVARIATE NORMALITY', STATISTICS & PROBABILITY LETTERS, 6 407-412 (1988)
DOI 10.1016/0167-7152(88)90100-9
Citations Scopus - 7Web of Science - 4
1988 RAYNER JCW, BEST DJ, 'SMOOTH TESTS OF GOODNESS OF FIT FOR REGULAR DISTRIBUTIONS', COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 17 3235-3267 (1988)
DOI 10.1080/03610928808829801
Citations Scopus - 6Web of Science - 5
1988 Rayner JCW, Seyb AJ, 'ANOVA Under Categorisation', Journal of Statistical Computation and Simulation, 29 181-193 (1988)

A basic assumption in the analysis of variance is that the observations are realisations of a univariate normal distribution. However, if the observations are rounded, the questio... [more]

A basic assumption in the analysis of variance is that the observations are realisations of a univariate normal distribution. However, if the observations are rounded, the question arises of how this affects the usual tests. Rayner, Dodds and Best (1986) considered a one factor fixed effects model with regard to simulated sizes and approximate asymptotic relative efficiencies. Here asymptotic relative efficiencies are considered for a three factor mixed effects model. The method generalises readily to other ANOVA models. © 1988 Taylor & Francis Group, LLC. All rights reserved.

DOI 10.1080/00949658808811061
Citations Scopus - 6
1987 MANLY BFJ, RAYNER JCW, 'THE COMPARISON OF SAMPLE COVARIANCE MATRICES USING LIKELIHOOD RATIO TESTS', BIOMETRIKA, 74 841-847 (1987)
Citations Scopus - 50Web of Science - 47
1987 BEST DJ, RAYNER JCW, 'WELCH APPROXIMATE SOLUTION FOR THE BEHRENS-FISHER PROBLEM', TECHNOMETRICS, 29 205-210 (1987)
DOI 10.2307/1269775
Citations Web of Science - 55
1987 BEST DJ, RAYNER JCW, 'GOODNESS-OF-FIT FOR GROUPED DATA USING COMPONENTS OF PEARSON-X2', COMPUTATIONAL STATISTICS & DATA ANALYSIS, 5 53-57 (1987)
DOI 10.1016/0167-9473(87)90007-7
Citations Scopus - 6Web of Science - 9
1987 Rayner JCW, Shanks JA, 'The redundant hypergeometric distribution', International Journal of Mathematical Education in Science and Technology, 18 287-295 (1987)

The redundant hypergeometric distribution results from a model similar to that for the ordinary hypergeometric, but where selections are made ¿redundantly¿. The distribution has... [more]

The redundant hypergeometric distribution results from a model similar to that for the ordinary hypergeometric, but where selections are made ¿redundantly¿. The distribution has applications in the area of statistical physics. However, the probability function is elementary and standard properties may be derived by familiar techniques. We anticipate therefore that the main use of the distribution may be as a source of novel but tractable exercises. © 1987 Taylor and Francis Group, LLC.

DOI 10.1080/0020739870180218
1987 Best DJ, Rayner JCW, 'Welch¿s approximate solution for the behrens¿fisher problem', Technometrics, 29 205-210 (1987)

The Wald, likelihood ratio, and score statistics have been calculated for the Behrens¿Fisher problem. These statistics provide asymptotically equivalent and weakly optimal tests.... [more]

The Wald, likelihood ratio, and score statistics have been calculated for the Behrens¿Fisher problem. These statistics provide asymptotically equivalent and weakly optimal tests. The test based on the Wald statistic was found to be very similar to the V test discussed by Welch (1937); hence the V test was compared with the likelihood ratio and score tests in a power study. Since the powers were very similar and the V test was more convenient to use from several points of view, we recommend this test. Sizes of the V test, as well as a power comparison with the usual pooled t test, were also obtained. © 1987 Taylor and Francis Group, LLC.

DOI 10.1080/00401706.1987.10488211
Citations Scopus - 55
1986 RAYNER JCW, BEST DJ, 'NEYMAN-TYPE SMOOTH TESTS FOR LOCATION-SCALE FAMILIES', BIOMETRIKA, 73 437-446 (1986)
Citations Scopus - 19Web of Science - 21
1986 RAYNER JCW, DODDS KG, BEST DJ, 'THE EFFECT OF CATEGORIZATION ON A SIMPLE ANALYSIS OF VARIANCE MODEL', BIOMETRICAL JOURNAL, 28 159-170 (1986)
DOI 10.1002/bimj.4710280205
Citations Scopus - 2Web of Science - 5
1985 RAYNER JCW, 'MAXIMUM-LIKELIHOOD ESTIMATION OF MU AND SIGMA FROM A MULTIVARIATE NORMAL-DISTRIBUTION', AMERICAN STATISTICIAN, 39 123-124 (1985)
DOI 10.2307/2682811
Citations Web of Science - 2
1985 RAYNER JCW, 'BIAS OF THE PEARSON CHI-SQUARED TEST', JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 21 329-331 (1985)
DOI 10.1080/00949658508810823
Citations Scopus - 2Web of Science - 2
1985 RAYNER JCW, MCINTYRE RI, 'USE OF THE SCORE STATISTIC FOR TESTING GOODNESS-OF-FIT OF SOME GENERALIZED DISTRIBUTIONS', BIOMETRICAL JOURNAL, 27 159-166 (1985)
DOI 10.1002/bimj.4710270207
Citations Scopus - 1Web of Science - 3
1985 BEST DJ, RAYNER JCW, 'A COMPARISON OF THE MPN AND FISHER-YATES ESTIMATORS FOR THE DENSITY OF ORGANISMS', BIOMETRICAL JOURNAL, 27 167-172 (1985)
DOI 10.1002/bimj.4710270208
Citations Web of Science - 7
1985 RAYNER JCW, BEST DJ, 'THE EFFECT OF CATEGORIZATION ON TESTING FOR AN EXPONENTIAL SCALE SHIFT', JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 11 197-206 (1985)
DOI 10.1016/0378-3758(85)90006-0
Citations Scopus - 3Web of Science - 1
1985 BEST DJ, RAYNER JCW, 'LANCASTERS TEST OF NORMALITY', JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 12 395-400 (1985)
DOI 10.1016/0378-3758(85)90088-6
Citations Scopus - 6Web of Science - 6
1985 BEST DJ, RAYNER JCW, 'UNIFORMITY TESTING WHEN ALTERNATIVES HAVE LOW ORDER', SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES A, 47 25-35 (1985)
Citations Web of Science - 5
1985 Rayner JCW, Best DJ, Dodds KG, 'THE CONSTRUCTION OF THE SIMPLE X2 AND NEYMAN SMOOTH GOODNESS OF FIT TESTS', Statistica Neerlandica, 39 35-50 (1985)

Suppose we wish to test whether data are consistent with a completely specified continuous distribution against a general alternative. Familiar omnibus tests are PEARSON'S X2 test... [more]

Suppose we wish to test whether data are consistent with a completely specified continuous distribution against a general alternative. Familiar omnibus tests are PEARSON'S X2 test and NEYMAN'S smooth test. Fundamental problems in the application of these tests are the construction and number of classes to use for X2, and the choice of the order of the NEYMAN smooth test. This paper examines these questions. Copyright © 1985, Wiley Blackwell. All rights reserved

DOI 10.1111/j.1467-9574.1985.tb01123.x
Citations Scopus - 7
1985 Rayner JCW, 'Maximum likelihood estimation of µ and Sfrom a multivariate normal distribution', American Statistician, 39 123-124 (1985)

In finding the maximum likelihood estimators of the parameters of a multivariate normal distribution, the following derivation first diagonalizes the covariance matrix and then ma... [more]

In finding the maximum likelihood estimators of the parameters of a multivariate normal distribution, the following derivation first diagonalizes the covariance matrix and then maximizes the likelihood by the choice of the elements of the transformed mean and the latent roots of the covariance matrix. Multivariate calculus is used to verify quickly and simply that the likelihood is indeed maximized. © 1985 Taylor & Francis Group, LLC.

DOI 10.1080/00031305.1985.10479410
1982 RAYNER JCW, 'CONSTRUCTING OPTIMAL UNIVARIATE TESTS', COMMUNICATIONS IN STATISTICS PART A-THEORY AND METHODS, 11 1903-1917 (1982)
DOI 10.1080/03610928208828359
1981 BEST DJ, RAYNER JCW, 'A NOTE ON MINEO GROUPING METHOD FOR THE CHI-SQUARE TEST OF GOODNESS OF FIT', SCANDINAVIAN JOURNAL OF STATISTICS, 8 185-186 (1981)
1981 Best DJ, Rayner JCW, 'Are Two Classes Enough for the X2Goodness of Fit Test?', Statistica Neerlandica, 35 157-163 (1981)

The chi-squared goodness of fit test (also known as the PearsonX2test) is often used to test whether data are consistent with a specified continuous distribution. The value of X2(... [more]

The chi-squared goodness of fit test (also known as the PearsonX2test) is often used to test whether data are consistent with a specified continuous distribution. The value of X2(and hence its associated probability level) can be altered by the choice of (i) the number of classes and (ii) the class probabilities. The effect on the power of the X2test of varying the number of classes when class probabilities are chosen to be equal is investigated. Copyright © 1981, Wiley Blackwell. All rights reserved

DOI 10.1111/j.1467-9574.1981.tb00724.x
Citations Scopus - 2
1975 RAYNER JCW, 'VARIANCE BOUNDS', SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES B, 37 135-138 (1975)
Citations Web of Science - 1
Show 114 more journal articles

Review (1 outputs)

Year Citation Altmetrics Link
2015 Rayner JCW, Thas O, Best DJ, 'Statistical Distribution Models: Goodness of Fit Tests (2015)
Co-authors John Best

Conference (11 outputs)

Year Citation Altmetrics Link
2011 Rippon PG, Rayner JC, 'Assessing Poisson and logistic regression models using smooth tests', Proceedings of the 4th Applied Statistics Education and Research Collaboration (ASEARC) Conference (2011) [E1]
Co-authors Paul Rippon
2011 Rayner JC, Best DJ, 'Nonparametric tests for two factor designs with an application to latin squares', Proceedings of the 4th Applied Statistics Education and Research Collaboration (ASEARC) Conference (2011) [E1]
Co-authors John Best
2011 Best DJ, Rayner JC, Thas O, 'Smooth tests of fit for a mixture of two Poisson distributions', Proceedings of the 4th Applied Statistics Education and Research Collaboration (ASEARC) Conference (2011) [E1]
Co-authors John Best
2011 Allingham D, Rayner JC, 'Two-Sample testing for equality of variances', Proceedings of the 4th Applied Statistics Education and Research Collaboration (ASEARC) Conference (2011) [E1]
2009 Best DJ, Rayner JC, Thas O, 'Nonparametric tests for randomized block data with ties and ordered alternatives', ASEARC: Proceedings of the Third Annual ASEARC Research Conference (2009) [E1]
Co-authors John Best
2009 Rayner JC, Rippon PG, 'Testing the poisson regression model', ASEARC: Proceedings of the Third Annual ASEARC Research Conference (2009) [E1]
Co-authors Paul Rippon
2008 Best DJ, Rayner JC, Thas O, 'Tests of fit for the beta binomial distribution', JSM 2008 Abstract Book (2008) [E3]
Co-authors John Best
2003 Davy PD, Rayner JCW, Beh EJ, 'Generalised correlations and Simpson's paradox', Current Research on Modelling, Data Mining and Quantitative Techniques (2003)
Co-authors Eric Beh
2001 Best DJ, Rayner JCW, 'Application of the Stuart test to sensory evaluation data', FOOD QUALITY AND PREFERENCE (2001)
DOI 10.1016/S0950-3293(01)00024-6
Citations Scopus - 5Web of Science - 6
2001 Gulati CM, Best DJ, Mather K, Lin X-Y, Rayner JC, Mishra SN, 'Advances in Statistics, Combinatorics and Related Areas' (2001) [E1]
2000 Best DJ, Rayner JCW, O'Sullivan MG, 'Product maps for consumer categorical data', FOOD QUALITY AND PREFERENCE (2000)
DOI 10.1016/S0950-3293(99)00044-0
Citations Scopus - 4Web of Science - 4
Show 8 more conferences
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Grants and Funding

Summary

Number of grants 5
Total funding $6,525,320

Click on a grant title below to expand the full details for that specific grant.


20082 grants / $5,580,000

Centre for Complex Dynamic Systems and Control$5,400,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Emeritus Laureate Professor Graham Goodwin, Professor Minyue Fu, Professor Reza Moheimani, Doctor Julio Braslavsky, Dr GREG Adams, Associate Professor Jose De Dona, Doctor Maria Seron, Doctor James Welsh, Doctor Andrew Fleming, Associate Professor Tristan Perez, Doctor Damian Marelli, Associate Professor Brailey Sims, Conjoint Professor Kerrie Mengersen, Professor A Pettitt, Dr R Reeves, Professor Ian Turner, Dr Salvatore Crisafulli, Dr M Downey, Mr J Lee, Mr P Stone, Conjoint Professor John Rayner
Scheme ARC Centres of Excellence
Role Investigator
Funding Start 2008
Funding Finish 2010
GNo G0188623
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

CDSC Sub-Account: Statistical Inference and Modelling$180,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Emeritus Laureate Professor Graham Goodwin, Conjoint Professor John Rayner
Scheme ARC Centres of Excellence
Role Investigator
Funding Start 2008
Funding Finish 2010
GNo GS090008
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20072 grants / $943,993

Applied Statistics Education and Research Collaboration$934,005

 

Funding body: Department of Education, Science and Training

Funding body Department of Education, Science and Training
Project Team

Professor David Steel

Scheme Collaboration and Structural Reform Fund
Role Investigator
Funding Start 2007
Funding Finish 2007
GNo
Type Of Funding Not Known
Category UNKN
UON N

Assessing Statistical Models Using Smooth Tests$9,988

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Conjoint Professor John Rayner
Scheme New Staff Grant
Role Lead
Funding Start 2007
Funding Finish 2007
GNo G0187560
Type Of Funding Internal
Category INTE
UON Y

20061 grants / $1,327

Australian Statistical Conference ASC/NZSA 2006 3-7 July 2006$1,327

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Conjoint Professor John Rayner
Scheme Travel Grant
Role Lead
Funding Start 2006
Funding Finish 2006
GNo G0186501
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Number of supervisions

Completed4
Current0

Past Supervision

Year Level of Study Research Title / Program / Supervisor Type
2013 PhD Application of Smooth Tests of Goodness of Fit to Generalized Linear Models
PhD (Statistics), Faculty of Science and Information Technology, The University of Newcastle
Co-Supervisor
2007 PhD Estimation of the Binomial Parameter: In Defence of Bayes (1763)
PhD (Statistics), Faculty of Science and Information Technology, The University of Newcastle
Principal Supervisor
2005 Honours An Empirical Study into the Distribution of All-Ordinaries Index Stock
Statistics, University of Wollongong
Co-Supervisor
2003 Honours A smooth test of goodness of fit for the zero-inflated Poisson distribution
Statistics, University of Wollongong
Sole Supervisor
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Conjoint Professor John Rayner

Position

Conjoint Professor
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Focus area

Statistics

Contact Details

Email john.rayner@newcastle.edu.au
Phone (02) 4921 5737
Fax (02) 4921 6898

Office

Room V126
Building Mathematics
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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