Statistical Theory: A Concise Introduction

Designed for a one-semester advanced undergraduate or graduate statistical theory course, Statistical Theory: A Concise Introduction, Second Edition clearly explains the underlying ideas, mathematics, and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, linear models, nonparametric statistics, and elements of decision theory. It introduces these topics on a clear intuitive level using illustrative examples in addition to the formal definitions, theorems, and proofs.

Based on the authors' lecture notes, the book is self-contained, which maintains a proper balance between the clarity and rigor of exposition. In a few cases, the authors present a sketched version of a proof, explaining its main ideas rather than giving detailed technical mathematical and probabilistic arguments.

Features:

• Second edition has been updated with a new chapter on Nonparametric Estimation; a significant update to the chapter on Statistical Decision Theory; and other updates throughout
• No requirement for heavy calculus, and simple questions throughout the text help students check their understanding of the material
• Each chapter also includes a set of exercises that range in level of difficulty
• Self-contained, and can be used by the students to understand the theory
• Chapters and sections marked by asterisks contain more advanced topics and may be omitted
• Special chapters on linear models and nonparametric statistics show how the main theoretical concepts can be applied to well-known and frequently used statistical tools

The primary audience for the book is students who want to understand the theoretical basis of mathematical statistics--either advanced undergraduate or graduate students. It will also be an excellent reference for researchers from statistics and other quantitative disciplines.

《統計理論：簡明入門，第二版》是為一學期的高年級本科生或研究生統計理論課程而設計的。本書清晰地解釋了主要統計概念的基本思想、數學和原則，包括參數估計、置信區間、假設檢驗、漸近分析、貝葉斯推斷、線性模型、非參數統計和決策理論的要素。除了正式的定義、定理和證明外，本書還通過實例來直觀地介紹這些主題。

本書基於作者的講義，是自成體系的，保持了清晰和嚴謹的表達之間的適當平衡。在一些情況下，作者提供了一個概要版本的證明，解釋其主要思想，而不是提供詳細的技術數學和概率論論證。

特點：
- 第二版新增了一章《非參數估計》和對《統計決策理論》一章的重大更新，並在全書中進行了其他更新。
- 不需要繁重的微積分，並且正文中的簡單問題有助於學生檢查對材料的理解。
- 每章還包括一組練習題，難度各不相同。
- 自成體系，學生可以用來理解理論。
- 用星號標記的章節包含更高級的主題，可以省略。
- 關於線性模型和非參數統計的特殊章節展示了如何將主要的理論概念應用於眾所周知且常用的統計工具。

本書的主要讀者是希望理解數學統計理論基礎的學生，包括高年級本科生和研究生。對於統計學和其他定量學科的研究人員來說，本書也是一本優秀的參考書。

Felix Abramovich is a professor at the Department of Statistics and Operations Research at Tel Aviv University.

Ya'acov Ritov is a professor in the Department of Statistics at the University of Michigan, Ann Arbor. He is a professor emeritus of Statistics at the Hebrew University of Jerusalem.

Felix Abramovich 是特拉維夫大學統計與運籌研究系的教授。

Ya'acov Ritov 是密西根大學安娜堡分校統計系的教授。他也是希伯來大學統計學的名譽教授。