Statistical Tests of Nonparametric Hypotheses Asymptotic Theory

1. Introduction. 1.1. Definitions. 1.2. Rank tests and empirical distribution functions. 1.3. Hypotheses of the tests. 1.4. Weak convergence of the test statistics. 1.5. Tests for densities and curves. 1.6. Asymptotic levels of tests. 1.7. Permutation and bootstrap tests. 1.8. Relative efficiency of tests -- 2. Asymptotic theory. 2.1. Parametric tests. 2.2. Parametric likelihood ratio tests. 2.3. Likelihood ratio tests against local alternatives. 2.4. Nonparametric likelihood ratio tests. 2.5. Nonparametric tests for empirical functionals. 2.6. Tests of homogeneity. 2.7. Mixtures of exponential distributions. 2.8. Nonparametric bootstrap tests. 2.9. Exercises -- 3. Nonparametric tests for one sample. 3.1. Introduction. 3.2. Kolmogorov-Smirnov tests for a distribution function. 3.3. Tests for symmetry of a density. 3.4. Tests about the form of a density. 3.5. Goodness of fit test in biased length models. 3.6. Goodness of fit tests for a regression function. 3.7. Tests about the form of a regression function. 3.8. Tests based on observations by intervals. 3.9. Exercises -- 4. Two-sample tests. 4.1. Introduction. 4.2. Tests of independence. 4.3. Test of homogeneity. 4.4. Goodness of fit tests in [symbol]. 4.5. Tests of symmetry for a bivariate density. 4.6. Tests about the form of densities. 4.7. Comparison of two regression curves. 4.8. Tests based on observations by intervals. 4.9. Exercises -- 5. Multi-dimensional tests. 5.1. Introduction. 5.2. Tests of independence. 5.3. Test of homogeneity of k sub-samples. 5.4. Test of homogeneity of k rescaled distributions. 5.5. Test of homogeneity of several variables of [symbol]. 5.6. Test of equality of marginal distributions. 5.7. Test of exchangeable components for a random variable. 5.8. Tests in single-index models. 5.9. Comparison of k curves. 5.10. Tests in proportional odds models. 5.11. Tests for observations by intervals. 5.12. Competing risks. 5.13. Tests for Markov renewal processes. 5.14. Tests in [symbol] as k[symbol] tends to infinity. 5.15. Exercises