Mathematical Statistics, 2nd Edition

This textbook provides a broad and solid introduction to mathematical statistics, including the classical subjects hypothesis testing, normal regression analysis, and normal analysis of variance. In addition, non-parametric statistics and vectorial statistics are considered, as well as applications of stochastic analysis in modern statistics, e.g., Kolmogorov-Smirnov testing, smoothing techniques, robustness and density estimation. For students with some elementary mathematical background. With many exercises. Updated, complete Solutions Manual available on request Prerequisites from measure theory and linear algebra are presented.

Table of Contents

Chapter 1. Probability theory
Chapter 2. Statistics and their probability distributions, estimation theory
Chapter 3. Hypothesis tests
Chapter 4. Simple regression analysis
Chapter 5. Normal analysis of variance
Chapter 6. Non-parametric methods
Chapter 7. Stochastic analysis and its applications in statistics
Chapter 8. Vectorial statistics
Appendix A. Lebesgue’s convergence theorems
Appendix B. Product measures
Appendix C. Conditional probabilities
Appendix D. The characteristic function of the Cauchy distribution
Appendix E. Metric spaces, equicontinuity
Appendix F. The Fourier transform and the existence of stoutly tailed distributions