Statistical Inference, 2/e

George Casella, Roger L. Berger

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Description

This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.

Table of Contents

1. PROBABILITY THEORY. Set Theory. Probability Theory. Conditional Probability and Independence. Random Variables. Distribution Functions. Density and Mass Functions. Exercises. Miscellanea.

2. TRANSFORMATION AND EXPECTATIONS. Distribution of Functions of a Random Variable. Expected Values. Moments and Moment Generating Functions. Differentiating Under an Integral Sign. Exercises. Miscellanea.

3. COMMON FAMILIES OF DISTRIBUTIONS. Introductions. Discrete Distributions. Continuous Distributions. Exponential Families. Locations and Scale Families. Inequalities and Identities. Exercises. Miscellanea.

 4. MULTIPLE RANDOM VARIABLES. Joint and Marginal Distributions. Conditional Distributions and Independence. Bivariate Transformations. Hierarchical Models and Mixture Distributions. Covariance and Correlation. Multivariate Distributions. Inequalities. Exercises. Miscellanea.

5. PROPERTIES OF A RANDOM SAMPLE. Basic Concepts of Random Samples. Sums of Random Variables from a Random Sample. Sampling for the Normal Distribution. Order Statistics. Convergence Concepts. Generating a Random Sample. Exercises. Miscellanea.

6. PRINCIPLES OF DATA REDUCTION. Introduction. The Sufficiency Principle. The Likelihood Principle. The Equivariance Principle. Exercises. Miscellanea.

7. POINT EXTIMATION. Introduction. Methods of Finding Estimators. Methods of Evaluating Estimators. Exercises. Miscellanea.

8. HYPOTHESIS TESTING. Introduction. Methods of Finding Tests. Methods of Evaluating Test. Exercises. Miscellanea.

9. INTERVAL ESTIMATION. Introduction. Methods of Finding Interval Estimators. Methods of Evaluating Interval Estimators. Exercises. Miscellanea.

10. ASYMPTOTIC EVALUATIONS. Point Estimation. Robustness. Hypothesis Testing. Interval Estimation. Exercises. Miscellanea.

11. ANALYSIS OF VARIANCE AND REGRESSION. Introduction. One-way Analysis of Variance. Simple Linear Regression. Exercises. Miscellanea.

12. REGRESSION MODELS. Introduction. Regression with Errors in Variables. Logistic Regression. Robust Regression. Exercises. Miscellanea. Appendix. Computer Algebra. References.

商品描述(中文翻譯)

描述

這本書從概率論的基本原理出發,建立了理論統計學。作者們從概率的基礎開始,使用統計技術、定義和概念來發展統計推斷的理論,這些技術、定義和概念是統計學的自然延伸和前一概念的結果。本書適用於研究生的第一年級學生,也可用於數學基礎扎實的統計學專業學生。它也可以以更強調統計理論的實際應用的方式使用,更關注對基本統計概念的理解和導出各種情況下合理的統計程序,而較少關注正式的最佳性研究。

目錄

1. 概率論。集合論。概率論。條件概率和獨立性。隨機變量。分佈函數。密度和質量函數。練習。雜項。

2. 變換和期望。隨機變量的函數分佈。期望值。矩和矩生成函數。在積分符號下求導數。練習。雜項。

3. 常見的分佈族。介紹。離散分佈。連續分佈。指數族。位置和尺度族。不等式和恆等式。練習。雜項。

4. 多個隨機變量。聯合和邊緣分佈。條件分佈和獨立性。雙變量變換。階層模型和混合分佈。協方差和相關性。多變量分佈。不等式。練習。雜項。

5. 隨機樣本的性質。隨機樣本的基本概念。從隨機樣本中的隨機變量的和。正態分佈的抽樣。順序統計量。收斂概念。生成隨機樣本。練習。雜項。

6. 數據縮減原則。介紹。充分性原則。似然原則。等變性原則。練習。雜項。

7. 點估計。介紹。找到估計量的方法。評估估計量的方法。練習。雜項。

8. 假設檢驗。介紹。找到檢驗方法。評估檢驗方法。練習。雜項。

9. 區間估計。介紹。找到區間估計量的方法。評估區間估計量的方法。練習。雜項。

10. 漸近評估。點估計。魯棒性。假設檢驗。區間估計。練習。雜項。

11. 方差分析和回歸。介紹。單因素方差分析。簡單線性回歸。練習。雜項。

12. 回歸模型。介紹。變量中的誤差回歸。邏輯回歸。魯棒回歸。練習。雜項。附錄。計算機代數。參考文獻。