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E-book
Author Nikulin, Mikhail S

Title Chi-Squared Goodness-of-Fit Tests for Censored Data
Published Somerset : John Wiley & Sons, Incorporated, 2017
©2018
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Description 1 online resource (165 pages)
Contents Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Introduction -- 1. Chi-squared Goodness-of-fit Tests for Complete Data -- 1.1. Classical Pearson's chi-squared test -- 1.2. Joint distribution of Xn(<U+006b>*n) and n(<U+006b>*n -- <U+006b>) -- 1.3. Parameter estimation based on complete data. Lemma of Chernoff and Lehmann -- 1.4. Parameter estimation based on grouped data. Theorem of Fisher -- 1.5. Nikulin-Rao-Robson chi-squared test -- 1.6. Other modifications -- 1.7. The choice of grouping intervals -- 2. Chi-squared Test for Censored Data -- 2.1. Generalized Pearson-Fisher chi-squared test -- 2.2. Maximum likelihood estimators for censored data -- 2.3. Nikulin-Rao-Robson chi-squared test for censored data -- 2.4. The choice of grouping intervals -- 2.4.1. Equifrequent grouping (EFG) -- 2.4.2. Intervals with equal expected numbers of failures (EENFG) -- 2.4.3. Optimal grouping (OptG) -- 2.5. Chi-squared tests for specific families of distributions -- 2.5.1. Exponential distribution -- 2.5.2. Weibull distribution -- 2.5.3. Lognormal distribution -- 2.5.4. Loglogistic distribution -- 2.5.5. Gompertz distribution -- 3. Comparison of the Chi-squared Goodness-of-fit Test with Other Tests -- 3.1. Tests based on the difference between non-parametric and parametric estimators -- 3.2. Comparison of goodness-of-fit tests for complete data -- 3.3. Comparison of goodness-of-fit tests for censored data -- 3.3.1. Lognormal-generalized Weibull pair of competing hypotheses -- 3.3.2. Exponential-Weibull pair of competing hypotheses -- 3.3.3. Weibull-generalized Weibull pairs of competing hypotheses -- 4. Chi-squared Goodness-of-fit Tests for Regression Models -- 4.1. Data and the idea of chi-squared test construction -- 4.2. Asymptotic distribution of the random vector Z -- 4.3. Test statistic -- 4.4. Choice of random grouping intervals
4.4.1. Test for the exponential AFT model -- 4.4.2. Tests for the scale-shape AFT models with constant covariates -- 4.4.3. Test for the Weibull AFT model with step-stresses -- APPENDICES -- Appendix 1. Tables of Asymptotically D-optimal Grouping -- Appendix 2. Data Sets -- Bibliography -- Index -- Other titles from iSTE in Mathematics and Statistics -- EULA
Notes Publisher supplied metadata and other sources
Form Electronic book
Author Chimitova, Ekaterina V
ISBN 1119427614
9781119427612