# Introduction to Mathematical Statistics, 8th edition

• Robert V. Hogg
• Joseph W. McKean
• Allen T. Craig

8th edition

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## Overview

For courses in mathematical statistics.

Comprehensive coverage of mathematical statistics — with a proven approach

Introduction to Mathematical Statistics by Hogg, McKean, and Craig enhances student comprehension and retention with numerous, illustrative examples and exercises. Classical statistical inference procedures in estimation and testing are explored extensively, and the text’s flexible organization makes it ideal for a range of mathematical statistics courses.

Substantial changes to the 8th Edition — many based on user feedback — help students appreciate the connection between statistical theory and statistical practice, while other changes enhance the development and discussion of the statistical theory presented.

0134686993 / 9780134686998  Introduction to Mathematical Statistics, 8/e

(Note: Sections marked with an asterisk * are optional.)

1. Probability and Distributions

1.1 Introduction

1.2 Sets

1.3 The Probability Set Function

1.4 Conditional Probability and Independence

1.5 Random Variables

1.6 Discrete Random Variables

1.7 Continuous Random Variables

1.8 Expectation of a Random Variable

1.9 Some Special Expectations

1.10 Important Inequalities

2. Multivariate Distributions

2.1 Distributions of Two Random Variables

2.2 Transformations: Bivariate Random Variables

2.3 Conditional Distributions and Expectations

2.4 Independent Random Variables

2.5 The Correlation Coefficient

2.6 Extension to Several Random Variables

2.7 Transformations for Several Random Variables

2.8 Linear Combinations of Random Variables

3. Some Special Distributions

3.1 The Binomial and Related Distributions

3.2 The Poisson Distribution

3.3 The Γ, χ2, and β Distributions

3.4 The Normal Distribution

3.5 The Multivariate Normal Distribution

3.6 t- and F-Distributions

3.7 Mixture Distributions*

4. Some Elementary Statistical Inferences

4.1 Sampling and Statistics

4.2 Confidence Intervals

4.3 ∗Confidence Intervals for Parameters of Discrete Distributions

4.4 Order Statistics

4.5 Introduction to Hypothesis Testing

4.7 Chi-Square Tests

4.8 The Method of Monte Carlo

4.9 Bootstrap Procedures

4.10 Tolerance Limits for Distributions*

5. Consistency and Limiting Distributions

5.1 Convergence in Probability

5.2 Convergence in Distribution

5.3 Central Limit Theorem

5.4 Extensions to Multivariate Distributions*

6. Maximum Likelihood Methods

6.1 Maximum Likelihood Estimation

6.2 Rao—Cramér Lower Bound and Efficiency

6.3 Maximum Likelihood Tests

6.4 Multiparameter Case: Estimation

6.5 Multiparameter Case: Testing

6.6 The EM Algorithm

7. Sufficiency

7.1 Measures of Quality of Estimators

7.2 A Sufficient Statistic for a Parameter

7.3 Properties of a Sufficient Statistic

7.4 Completeness and Uniqueness

7.5 The Exponential Class of Distributions

7.6 Functions of a Parameter

7.7 The Case of Several Parameters

7.8 Minimal Sufficiency and Ancillary Statistics

7.9 Sufficiency, Completeness, and Independence

8. Optimal Tests of Hypotheses

8.1 Most Powerful Tests

8.2 Uniformly Most Powerful Tests

8.3 Likelihood Ratio Tests

8.3.2 Likelihood Ratio Tests for Testing Variances of Normal Distributions

8.4 The Sequential Probability Ratio Test*

8.5 Minimax and Classification Procedures*

9. Inferences About Normal Linear Models

9.1 Introduction

9.2 One-Way ANOVA

9.3 Noncentral χ2 and F-Distributions

9.4 Multiple Comparisons

9.5 Two-Way ANOVA

9.6 A Regression Problem

9.7 A Test of Independence

9.8 The Distributions of Certain Quadratic Forms

9.9 The Independence of Certain Quadratic Forms

10. Nonparametric and Robust Statistics

10.1 Location Models

10.2 Sample Median and the Sign Test

10.3 Signed-Rank Wilcoxon

10.4 Mann—Whitney—Wilcoxon Procedure

10.5 General Rank Scores*

10.7 Simple Linear Model

10.8 Measures of Association

10.9 Robust Concepts

11. Bayesian Statistics

11.1 Bayesian Procedures

11.2 More Bayesian Terminology and Ideas

11.3 Gibbs Sampler

11.4 Modern Bayesian Methods

Appendices:

A.1 Regularity Conditions

A.2 Sequences

B. R Primer

B.1 Basics

B.2 Probability Distributions

B.3 R Functions

B.4 Loops

B.5 Input and Output

B.6 Packages

C. Lists of Common Distributions

D. Table of Distributions

E. References