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.
1. Chi-squared Goodness-of-fit Tests for Complete Data.
2. Chi-squared Test for Censored Data.
3. Comparison of the Chi-squared Goodness-of-fit Test with Other Tests.
4. Chi-squared Goodness-of-fit Tests for Regression Models.
Mikhail S. Nikulin is Emeritus Professor at the University Victor Segalen, and a member of the Institute of Mathematics at Bordeaux, France. His research and teaching activities concern mathematical statistics and its applications in reliability and survival analysis.
Ekaterina V. Chimitova is Associate Professor at Novosibirsk State Technical University, Russia. Her research and teaching activities concern mathematical statistics and the application of computer simulation techniques for investigation of statistical regularities and data analysis.
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