Mathematical Basis of Statistics : Probability and Mathematical Statistics: A Series of Monographs and Textbooks

Mathematical Basis of Statistics provides information pertinent to the methods and the mathematical basis of statistics. This book discusses the fundamental notion of statistical space. Organized into 12 chapters, this book begins with an overview of the notion of statistical space in mathematical statistics and discusses other analogies with probability theory. This text then presents the notions of sufficiency and freedom, which are fundamental and useful in statistics but do not correspond to any notion in probability theory. Other chapters consider the theory of nonsequential tests and explain the practical meaning of the mathematical tools employed in statistics. This book discusses as well distributions used most frequently in classical statistical problems based on the normal distribution and provides relationships among these distributions. The final chapter deals with certain problems of mathematical statistics that are related to various problems of functional analysis. This book is a valuable resource for graduate and postgraduate students. Content: Front Matter, Page iii Dedication, Page iv Copyright, Page iv Foreword, Page ix Editor's Preface, Pages xi-xii Preface, Pages xiii-xiv Notation and Terminology, Pages xv-xvi CHAPTER 1 - Statistical Spaces, Pages 1-11 CHAPTER 2 - Sufficiency and Freedom, Pages 12-31 CHAPTER 3 - Statistical Information, Pages 32-40 CHAPTER 4 - Statistical Inference, Pages 41-52 CHAPTER 5 - Testing Statistical Hypotheses, Pages 53-75 CHAPTER 6 - Statistical Estimation, Pages 76-87 CHAPTER 7 - The Multivariate Normal Distribution, Pages 88-102 CHAPTER 8 - Random Matrices, Pages 103-132 CHAPTER 9 - Linear-Normal Statistical Spaces, Pages 133-170 CHAPTER 10 - Exponential Statistical Spaces, Pages 171-184 CHAPTER 11 - Testing Hypotheses on Exponential Statistical Spaces, Pages 185-203 CHAPTER 12 - Functional Analysis and Mathematical Statistics, Pages 204-227 APPENDIX - Conditional Probability, Pages 229-242 References, Pages 243-245 Index, Pages 247-249 Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Pages ibc1-ibc2 Jean-rené Barra ; Translation Edited By Leon Herbach. Translation Of: Notions Fondamentales De Statistique Mathématique. Includes Index. Bibliography: P. 243-245.