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

Mikhail S. Nikulin, University Victor Segalen, France.

• 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