Statistical Inference

✍ Scribed by George Casella, Roger L. Berger

• Publisher: Cengage Learning
• Year: 2001
• Tongue: English
• Leaves: 690
• Edition: 2
• Category: Library

✦ Synopsis

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. This book can be used for readers 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

Cover
Preface to the Second Edition
Preface to the First Edition
Contents
List of Tables
List of Figures
List of Examples
Chapter 1: Probability Theory
1.1 Set Theory
1.2 Basics of Probability Theory
1.3 Conditional Probability and Independence
1.4 Random Variables
1.5 Distribution Functions
1.6 Density and Mass Functions
1.7 Exercises
1.8 Miscellanea
Chapter 2: Transformations and Expectations
2.1 Distributions of Functions of a Random Variable
2.2 Expected Values
2.3 Moments and Moment Generating Functions
2.4 Differentiating under an Integral Sign
2.5 Exercises
2.6 Miscellanea
Chapter 3: Common Families of Distributions
3.1 Introduction
3.2 Discrete Distributions
3.3 Continuous Distributions
3.4 Exponential Families
3.5 Location and Scale Families
3.6 Inequalities and Identities
3.7 Exercises
3.8 Miscellanea
Chapter 4: Multiple Random Variables
4.1 Joint and Marginal Distributions
4.2 Conditional Distributions and Independence
4.3 Bivariate Transformations
4.4 Hierarchical Models and Mixture Distributions
4.5 Covariance and Correlation
4.6 Multivariate Distributions
4.7 Inequalities
4.8 Exercises
4.9 Miscellanea
Chapter 5: Properties of a Random Sample
5.1 Basic Concepts of Random Samples
5.2 Sums of Random Variables from a Random Sample
5.3 Sampling from the Normal Distribution
5.4 Order Statistics
5.5 Convergence Concepts
5.6 Generating a Random Sample
5.7 Exercises
5.8 Miscellanea
Chapter 6: Principles of Data Reduction
6.1 Introduction
6.2 The Sufficiency Principle
6.3 The Likelihood Principle
6.4 The Equivariance Principle
6.5 Exercises
6.6 Miscellanea
Chapter 7: Point Estimation
7.1 Introduction
7.2 Methods of Finding Estimators
7.3 Methods of Evaluating Estimators
7.4 Exercises
7.5 Miscellanea
Chapter 8: Hypothesis Testing
8.1 Introduction
8.2 Methods of Finding Tests
8.3 Methods of Evaluating Tests
8.4 Exercises
8.5 Miscellanea
Chapter 9: Interval Estimation
9.1 Introduction
9.2 Methods of Finding Interval Estimators
9.3 Methods of Evaluating Interval Estimators
9.4 Exercises
9.5 Miscellanea
Chapter 10: Asymptotic Evaluations
10.1 Point Estimation
10.2 Robustness
10.3 Hypothesis Testing
10.4 Interval Estimation
10.5 Exercises
10.6 Miscellanea
Chapter 11: Analysis of Variance and Regression
11.1 Introduction
11.2 Oneway Analysis of Variance
11.3 Simple Linear Regression
11.4 Exercises
11.5 Miscellanea
Chapter 12: Regression Models
12.1 Introduction
12.2 Regression with Errors in Variables
12.3 Logistic Regression
12.4 Robust Regression
12.5 Exercises
12.6 Miscellanea
Appendix: Computer Algebra
Table of Common Distributions
References
Author Index
Subject Index