Chi-squared Goodness-of-fit Tests for Censored Data by Ekaterina V. Chimitova (E

Description: FREE SHIPPING UK WIDE Chi-squared Goodness-of-fit Tests for Censored Data by Ekaterina V. Chimitova, Mikhail S. Nikulin 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Author Biography Mikhail S. Nikulin, University Victor Segalen, France. Table of Contents Introduction ix Chapter 1. Chi-squared Goodness-of-fit Tests for Complete Data 1 1.1. Classical Pearsons chi-squared test 1 1.2. Joint distribution of Xn(θ∗n)and√n(θ∗n−θ) 3 1.3. Parameter estimation based on complete data Lemma of Chernoff and Lehmann 5 1.4. Parameter estimation based on grouped data. Theorem of Fisher 10 1.5. Nikulin-Rao-Robson chi-squared test 12 1.6. Other modifications 18 1.7. The choice of grouping intervals 20 Chapter 2. Chi-squared Test for Censored Data 31 2.1. Generalized Pearson-Fisher chi-squared test 32 2.2. Maximum likelihood estimators for censored data 34 2.3. Nikulin-Rao-Robson chi-squared test for censored data 38 2.4. The choice of grouping intervals 45 2.4.1. Equifrequent grouping (EFG) 45 2.4.2. Intervals with equal expected numbers of failures (EENFG) 46 2.4.3. Optimal grouping (OptG) 48 2.5. Chi-squared tests for specific families of distributions 51 2.5.1. Exponential distribution 51 2.5.2. Weibull distribution 55 2.5.3. Lognormal distribution 60 2.5.4. Loglogistic distribution 63 2.5.5. Gompertz distribution 67 Chapter 3. Comparison of the Chi-squared Goodness-of-fit Test with Other Tests 71 3.1. Tests based on the difference between non-parametric and parametric estimators 71 3.2. Comparison of goodness-of-fit tests for complete data 76 3.3. Comparison of goodness-of-fit tests for censored data 79 3.3.1. Lognormal-generalized Weibull pair of competing hypotheses 80 3.3.2. Exponential-Weibull pair of competing hypotheses 82 3.3.3. Weibull-generalized Weibull pairs of competing hypotheses 84 Chapter 4. Chi-squared Goodness-of-fit Tests for Regression Models 87 4.1. Data and the idea of chi-squared test construction 89 4.2. Asymptotic distribution of the random vector Z 91 4.3. Test statistic 96 4.4. Choice of random grouping intervals 97 4.4.1. Test for the exponential AFT model 99 4.4.2. Tests for the scale-shape AFT models with constant covariates 101 4.4.3. Test for the Weibull AFT model with step-stresses 108 Appendices 111 Appendix 1 113 Appendix 2 125 Bibliography 131 Index 141 Details ISBN1786300001 ISBN-10 1786300001 ISBN-13 9781786300003 Short Title CHI-SQUARED GOODNESS-OF-FIT TE Language English Media Book Place of Publication London Country of Publication United Kingdom DEWEY 519.56 Author Mikhail S. Nikulin UK Release Date 2017-06-06 AU Release Date 2017-06-06 NZ Release Date 2017-06-06 Pages 158 Publisher ISTE Ltd and John Wiley & Sons Inc Year 2017 Format Paperback Publication Date 2017-06-06 Imprint ISTE Ltd and John Wiley & Sons Inc Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! 30 DAY RETURN POLICY No questions asked, 30 day returns! FREE DELIVERY No matter where you are in the UK, delivery is free. SECURE PAYMENT Peace of mind by paying through PayPal and eBay Buyer Protection TheNile_Item_ID:136272370;

Price: 197.54 GBP

Location: London

End Time: 2025-01-03T20:00:45.000Z

Shipping Cost: 2.33 GBP