Nonparametric Tests for Complete Data
by:Vilijandas Bagdonavièus, Julius Kruopis, Mikhail Nikulin
This book concerns testing hypotheses in non-parametric models. Classical non-parametric tests (goodness-of-fit, homogeneity, randomness, independence) of complete data are considered. Most of the test results are proved and real applications are illustrated using examples. Theories and exercises are provided. The incorrect use of many tests applying most statistical software is highlighted and discussed.
目录：
Chapter 1. Introduction
1.1. Statistical hypotheses
1.2. Examples of hypotheses in non-parametric models
1.3. Statistical tests
1.4. P-value
1.5. Continuity correction
1.6. Asymptotic relative efficiency
Chapter 2. Chi-squared Tests
2.1. Introduction
2.2. Pearson’s goodness-of-fit test: simple hypothesis
2.3. Pearson’s goodness-of-fit test: composite hypothesis
2.4. Modified chi-squared test for composite hypotheses
2.5. Chi-squared test for independence
2.6. Chi-squared test for homogeneity
2.7. Bibliographic notes
2.8. Exercises
2.9. Answers
Chapter 3. Goodness-of-fit Tests Based on Empirical Processes
3.1. Test statistics based on the empirical process
3.2. Kolmogorov–Smirnov test
3.3. ω2, Cramér–von-Mises and Andersen–Darling tests
3.4. Modifications of Kolmogorov–Smirnov, Cramér–von-Mises and Andersen–Darling tests: composite hypotheses
3.5. Two-sample tests
3.6. Bibliographic notes
3.7. Exercises
3.8. Answers
Chapter 4. Rank Tests
4.1. Introduction
4.2. Ranks and their properties
4.3. Rank tests for independence
4.4. Randomness tests
4.5. Rank homogeneity tests for two independent
4.6. Hypothesis on median value: the Wilcoxon signed ranks test
4.7. Wilcoxon’s signed ranks test for homogeneity of two related samples
4.8. Test for homogeneity of several independent samples: Kruskal–Wallis test
4.9. Homogeneity hypotheses for k related samples: Friedman test
4.10. Independence test based on Kendall’s concordance coefficient
4.11. Bibliographic notes
4.12. Exercises
4.13. Answers
Chapter 5. Other Non-parametric Tests
5.1. Sign test
5.2. Runs test
5.3. McNemar’s test
5.4. Cochran test
5.5. Special goodness-of-fit tests
5.6. Bibliographic notes
5.7. Exercises
5.8. Answers
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Nonparametric Tests for Censored Data
by:Vilijandas Bagdonavièus, Julius Kruopis, Mikhail Nikulin
This book concerns testing hypotheses in non-parametric models. Generalizations of many non-parametric tests to the case of censored and truncated data are considered. Most of the test results are proved and real applications are illustrated using examples. Theories and exercises are provided. The incorrect use of many tests applying most statistical software is highlighted and discussed.
目录：
Chapter 1. Censored and Truncated Data
1.1. Right-censored data
1.2. Left truncation
1.3. Left truncation and right censoring
1.4. Nelson–Aalen and Kaplan–Meier estimators
1.5. Bibliographic notes
Chapter 2. Chi-squared Tests
2.1. Chi-squared test for composite hypothesis
2.2. Chi-squared test for exponential distributions
2.3. Chi-squared tests for shape-scale distribution families
2.4. Chi-squared tests for other families
2.5. Exercises
2.6. Answers
Chapter 3. Homogeneity Tests for Independent Populations
3.1. Data
3.2. Weighted logrank statistics
3.3. Logrank test statistics as weighted sums of differences between observed and expected number of failures
3.4. Examples of weights
3.5. Weighted logrank statistics as modified score statistics
3.6. The first two moments of weighted logrank statistics
3.7. Asymptotic properties of weighted logrank statistics
3.8. Weighted logrank tests
3.9. Homogeneity testing when alternatives are crossings of survival functions
3.10. Exercises
3.11. Answers
Chapter 4. Homogeneity Tests for Related Populations
4.1. Paired samples
4.2. Logrank-type tests for homogeneity of related k > 2 samples
4.3. Homogeneity tests for related samples against crossing marginal survival functions alternatives
4.4. Exercises
4.5. Answers
Chapter 5. Goodness-of-fit for Regression Models
5.1. Goodness-of-fit for the semi-parametric Cox model
5.2. Chi-squared goodness-of-fit tests for parametric AFT models
5.3. Chi-squared test for the exponential AFT model
5.4. Chi-squared tests for scale-shape AFT models.
5.5. Bibliographic notes
5.6. Exercises
5.7. Answers
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