Mathematical Statistics

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.
• Prerequisites from measure theory and linear algebra are presented.
  

1;Preface;6 2;Contents;8 3;Chapter I. Probability theory;12 4;Chapter II. Statistics and their probability distributions, estimation theory;76 5;Chapter III. Hypothesis tests;166 6;Chapter IV. Simple regression analysis;211 7;Chapter V. Normal analysis of variance;240 8;Chapter VI. Non-parametric methods;261 9;Chapter VII. Stochastic analysis and its applications in statistics;293 10;Chapter VIII. Vectorial statistics;430 11;Appendix A. Lebesgues convergence theorems;540 12;Appendix B. Product measures;543 13;Appendix C. Conditional probabilities;547 14;Appendix D. The characteristic function of the Cauchy distribution;551 15;Appendix E. Metric spaces, equicontinuity;554 16;Appendix F. The Fourier transform and the existence of stoutly tailed distributions;564 17;List of elementary probability densities;570 18;Frequently used symbols;572 19;Statistical tables;579 20;Bibliography;598 21;Index;602