Chi-squared Goodness-of-fit Tests for Censored Data

AvMikhail S. Nikulin,Ekaterina V. Chimitova

Häftad, Engelska, 2017

1 749 kr

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Beskrivning

This book is devoted to the problems of construction and application of chi-squared goodness-of-fit tests for complete and censored data. Classical chi-squared tests assume that unknown distribution parameters are estimated using grouped data, but in practice this assumption is often forgotten. In this book, we consider modified chi-squared tests, which do not suffer from such a drawback. The authors provide examples of chi-squared tests for various distributions widely used in practice, and also consider chi-squared tests for the parametric proportional hazards model and accelerated failure time model, which are widely used in reliability and survival analysis. Particular attention is paid to the choice of grouping intervals and simulations.This book covers recent innovations in the field as well as important results previously only published in Russian. Chi-squared tests are compared with other goodness-of-fit tests (such as the Cramer-von Mises-Smirnov, Anderson-Darling and Zhang tests) in terms of power when testing close competing hypotheses.

Produktinformation

Utgivningsdatum:2017-06-06
Mått:160 x 231 x 10 mm
Vikt:249 g
Format:Häftad
Språk:Engelska
Antal sidor:158
Förlag:ISTE Ltd and John Wiley & Sons Inc
ISBN:9781786300003

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik

Mer om författaren

Mikhail S. Nikulin, University Victor Segalen, France.

Innehållsförteckning

Introduction ixChapter 1. Chi-squared Goodness-of-fit Tests for Complete Data 11.1. Classical Pearson’s chi-squared test 11.2. Joint distribution of Xn(θ∗n)and√n(θ∗n−θ) 31.3. Parameter estimation based on complete data Lemma of Chernoff and Lehmann 51.4. Parameter estimation based on grouped data. Theorem of Fisher 101.5. Nikulin-Rao-Robson chi-squared test 121.6. Other modifications 181.7. The choice of grouping intervals 20Chapter 2. Chi-squared Test for Censored Data 312.1. Generalized Pearson-Fisher chi-squared test 322.2. Maximum likelihood estimators for censored data 342.3. Nikulin-Rao-Robson chi-squared test for censored data 382.4. The choice of grouping intervals 452.4.1. Equifrequent grouping (EFG) 452.4.2. Intervals with equal expected numbers of failures (EENFG) 462.4.3. Optimal grouping (OptG) 482.5. Chi-squared tests for specific families of distributions 512.5.1. Exponential distribution 512.5.2. Weibull distribution 552.5.3. Lognormal distribution 602.5.4. Loglogistic distribution 632.5.5. Gompertz distribution 67Chapter 3. Comparison of the Chi-squared Goodness-of-fit Test with Other Tests 713.1. Tests based on the difference between non-parametric and parametric estimators 713.2. Comparison of goodness-of-fit tests for complete data 763.3. Comparison of goodness-of-fit tests for censored data 793.3.1. Lognormal-generalized Weibull pair of competing hypotheses 803.3.2. Exponential-Weibull pair of competing hypotheses 823.3.3. Weibull-generalized Weibull pairs of competing hypotheses 84Chapter 4. Chi-squared Goodness-of-fit Tests for Regression Models 874.1. Data and the idea of chi-squared test construction 894.2. Asymptotic distribution of the random vector Z 914.3. Test statistic 964.4. Choice of random grouping intervals 974.4.1. Test for the exponential AFT model 994.4.2. Tests for the scale-shape AFT models with constant covariates 1014.4.3. Test for the Weibull AFT model with step-stresses 108Appendices 111Appendix 1 113Appendix 2 125Bibliography 131Index 141