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Название: A Companion for Mathematical Statistics
Автор: Gentle J.
This document is directed toward students for whom mathematical statistics is or will become an important part of their lives. Obviously, such students should be able to work through the details of “hard” proofs and derivations. In addition, students at this level should acquire, or begin acquiring, a deep appreciation for the field, including its historical development and its relation to other areas of mathematics and science generally. Some of the chapter endnotes are intended to help students gain such an appreciation by leading them to background sources. It is important to understand the intellectual underpinnings of our science. There are certain principles (such as sufficiency, for example) that guide our approaches to statistical inference. There are various general approaches (see page 157) that we follow.Within these general approaches there are a number of specific methods (see page 157). The student should develop an appreciation for the relations between principles, approaches, and methods. It is of course expected that the student will read the primary textbook, as well as various other texts, and to work through all proofs and examples in the primary textbook. As a practical matter, obviously, even if I attempted to cover all of these in class, there just is not enough class time to do it. This book on mathematical statistics assumes a certain amount of background in mathematics. Following the final chapter on mathematical statistics Chapter 10, there is Chapter 0 on “statistical mathematics” (that is, mathematics with strong relevance to statistical theory) that provides much of the general mathematical background for probability and statistics. Chapter 0 grew (and is growing) recursively. Every time I add material, it seems that I need to add some background for the new material. This is obviously a game one cannot win