| Description |
1 online resource (x, 293 pages) : illustrations |
| Physical Medium |
polychrome |
| Description |
text file |
| Summary |
An overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman-Pearson and LeCam's theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models defining the distributions of point processes and diffusions. With many new test statistics developed for smooth curves, the reliance on kernel estimators with bias corrections and the weak convergence of the estimators are useful to prove the asymptotic properties of the tests, extending the coverage to semiparametric models. They include tests built from continuously observed processes and observations with cumulative intervals. |
| Bibliography |
Includes bibliographical references (pages 287-290) and index. |
| Contents |
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. |
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6. Nonparametric tests for processes. 6.1. Introduction. 6.2. Goodness of fit tests for an ergodic process. 6.3. Poisson process. 6.4. Poisson processes with scarce jumps. 6.5. Point processes in [symbol]. 6.6. Marked point processes. 6.7. Spatial Poisson processes. 6.8. Tests of stationarity for point processes. 6.9. Diffusion processes. 6.10. Comparison of diffusion processes. 6.11. Exercises -- 7. Nonparametric tests under censoring or truncation. 7.1. Introduction. 7.2. Comparison of right-censored distributions. 7.3. Likelihood ratio test of homogeneity. 7.4. Tests of homogeneity against general local alternatives. 7.5. Goodness of fit for the hazard functions ratio. 7.6. Tests of comparison of k samples. 7.7. Goodness of fit tests for k samples. 7.8. Tests of independence of two censored variables. 7.9. Comparison of two bivariate distributions. 7.10. Tests for left-censored samples. 7.11. Tests for the mean residual life and excess life. 7.12. Tests for right or left-truncated samples. 7.13. Comparison of censored or truncated regression curves. 7.14. Observation in random intervals. 7.15. Exercises -- 8. Sequential tests. 8.1. Introduction. 8.2. Definitions and properties. 8.3. Sequential likelihood ratio test. 8.4. Sequential algorithms for test statistics. 8.5. Properties of the record variables. 8.6. Sequential tests for point processes. 8.7. Sequential tests for hazard functions. 8.8. Sequential tests for regressions and diffusion processes. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Nonparametric statistics -- Asymptotic theory.
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Nonparametric statistics -- Asymptotic theory. |
| Genre/Form |
Electronic books.
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Llibres electrònics.
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Electronic books.
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| Subject |
Estadística d'ordre.
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Estadística no paramètrica.
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| Other Form: |
Print version: Pons, Odile. Statistical tests of nonparametric hypotheses. [Hackensack] New Jersey : World Scientific, [2014] 9789814531740 (DLC) 2013027370 (OCoLC)853113842 |
| ISBN |
9789814531757 (electronic book) |
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9814531758 (electronic book) |
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9789814531740 (hardcover ; alkaline paper) |
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981453174X (hardcover ; alkaline paper) |
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