Mathematical Statistics

This book provides a calculus-based introduction to mathematical statistics. The book integrates probability and statistics, distribution theory and inference, and estimation and hypothesis testing. It will serve as an important reference for students in statistics and applied disciplines.

Wide audience, it will serve as an important reference for anyone in statistics and the applied disciplines The book aims to be mathematically complete: every formula is derived, and every theorem proved at the appropriate level Each new concept is introduced and exemplified by interesting statistical problems; and more abstract concepts appear only gradually Emphasizes modeling of experimental data while avoiding abstract probability and distribution theory Users are led to do mathematical statistics, not just to appreciate it, with the assistance of 500 interesting exercises

Résumé
This textbook introduces the mathematical concepts and methods that underlie statistics. The book is committed to both a high level of mathematical seriousness and to an intimate connection with application. In its teaching style, the book is mathematically complete concrete constructive active.

Contenu
Getting Started.- Structural Models for Data.- Least Squares Methods.- Combinatorial Probability.- Other Probability Models.- Discrete Random Variables I: The Hypergeometric Process.- Discrete Random Variables II: The Bernoulli Process.- Random Vectors and Random Samples.- Maximum Likelihood Estimates for Discrete Models.- Continuous Random Variables I: The Gamma and Beta Families.- Continuous Random Variables II: Expectations and the Normal Family.- Continuous Random Vectors.- Sampling Statistics for the Linear Model.- Representing Distributions.