Nonparametric Tests for Complete Data

AvVilijandas Bagdonavicius,Julius Kruopis

Inbunden, Engelska, 2010

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Beskrivning

Statistical analysis of data sets usually involves construction of a statistical model of the distribution of data within the available sample – and by extension the distribution of all data of the same category in the world. Statistical models are either parametric or non-parametric – this distinction is based on whether or not the model can be described in terms of a finite-dimensional parameter – and the models must be tested to ascertain whether or not they conform to the data, or are accurate.This book addresses the testing of hypotheses in non-parametric models in the general case for complete data samples. Classical non-parametric tests (goodness-of-fit, homogeneity, randomness, independence) of complete data are considered, and explained. Tests featured include the chi-squared and modified chi-squared tests, rank and homogeneity tests, and most of the test results are proved, with real applications illustrated using examples. The incorrect use of many tests, and their application using commonly deployed statistical software is highlighted and discussed.

Produktinformation

Utgivningsdatum:2010-12-07
Mått:158 x 236 x 23 mm
Vikt:612 g
Format:Inbunden
Språk:Engelska
Antal sidor:320
Förlag:ISTE Ltd and John Wiley & Sons Inc
ISBN:9781848212695

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Vilijandas Bagdonavicius is Professor of Mathematics at the University of Vilnius in Lithuania. His main research areas are statistics, reliability and survival analysis. Julius Kruopis is Associate Professor of Mathematics at the University of Vilnius in Lithuania. His main research areas are statistics and quality control. Mikhail S. Nikulin is a member of the Institute of Mathematics in Bordeaux, France.

Innehållsförteckning

Preface xiTerms and Notation xvChapter 1. Introduction 11.1. Statistical hypotheses 11.2. Examples of hypotheses in non-parametric models 21.3. Statistical tests 51.4. P-value 71.5. Continuity correction 101.6. Asymptotic relative efficiency 13Chapter 2. Chi-squared Tests 172.1. Introduction 172.2. Pearson’s goodness-of-fit test: simple hypothesis 172.3. Pearson’s goodness-of-fit test: composite hypothesis 262.4. Modified chi-squared test for composite hypotheses 342.5. Chi-squared test for independence 522.6. Chi-squared test for homogeneity 572.7. Bibliographic notes 642.8. Exercises 642.9. Answers 72Chapter 3. Goodness-of-fit Tests Based on Empirical Processes 773.1. Test statistics based on the empirical process 773.2. Kolmogorov–Smirnov test 823.3. ω2, Cramér–von-Mises and Andersen–Darling tests 863.4. Modifications of Kolmogorov–Smirnov, Cramér–von-Mises and Andersen–Darling tests: compositehypotheses 913.5. Two-sample tests 983.6. Bibliographic notes 1043.7. Exercises1063.8. Answers 109Chapter 4. Rank Tests 1114.1. Introduction 1114.2. Ranks and their properties 1124.3. Rank tests for independence 1174.4. Randomness tests 1394.5. Rank homogeneity tests for two independent samples 1464.6. Hypothesis on median value: the Wilcoxon signed ranks test 1684.7. Wilcoxon’s signed ranks test for homogeneity of two related samples 1804.8. Test for homogeneity of several independent samples: Kruskal–Wallis test 1814.9. Homogeneity hypotheses for k related samples: Friedman test 1914.10. Independence test based on Kendall’s concordance coefficient 2044.11. Bibliographic notes 2084.12. Exercises 2094.13. Answers 212Chapter 5. Other Non-parametric Tests 2155.1. Sign test 2155.2. Runs test 2215.3. McNemar’s test 2315.4. Cochran test 2385.5. Special goodness-of-fit tests 2455.6. Bibliographic notes 2685.7. Exercises 2695.8. Answers 271APPENDICES 275Appendix A. Parametric Maximum Likelihood 277Appendix B. Notions from the Theory of 281BBibliography 293Index 305