A collection of problems and exercises on mathematical statistics. (Q2728732)

This book contains 460 problems and exercises on main parts of the standard educational course of mathematical statistics. A number of theoretical problems on the empirical distribution function, construction and properties of statistics, interval estimation, and testing hypotheses is given. Answers for all problems and exercises are given at the end of the book. The contents of the book are as follows:NEWLINENEWLINENEWLINEPart I. Empirical distributions. S~1. A sample and theory of order statistics. S~2. The empirical distribution function.NEWLINENEWLINENEWLINEPart II. Methods for obtaining estimators. S~3. The method of moments. S~4. The maximum-likelihood method. S~5. Bayesian estimators.NEWLINENEWLINENEWLINEPart III. The properties of estimators. S~6. Unbiased estimators. Consistency. S~7. Asymptotic normality.NEWLINENEWLINENEWLINEPart IV. On comparing estimators. S~8. Mean square approach. S~9. Asymptotic approach. S~10. Sufficient statistics. S~11. Complete estimators. S~12. Efficient estimators. S~13. The Rao-Cramér inequality.NEWLINENEWLINENEWLINEPart V. Interval estimation. S~14. Confidence intervals. S~15. Asymptotic confidence intervals.NEWLINENEWLINENEWLINEPart VI. Testing hypotheses. S~16. Testing of two simple hypotheses. S~17. Bayes and minimax tests. S~18. The most powerful tests. S~19. Unifomly most powerful tests. S~20. Goodness-of fit tests.NEWLINENEWLINENEWLINEPart VII. Problems for revision. S~21. Estimations of parameters. S~22. Testing hypotheses.NEWLINENEWLINENEWLINEApplications (examples of distributions and tables of the normal distribution, \(\chi^2\)-distribution, Student distribution and Kolmogorov distribution).