Introduction to Mathematical Statistics, Global Edition

Series
Pearson
Author
Robert V. Hogg / Joeseph McKean / Allen T Craig  
Publisher
Pearson
Cover
Softcover
Edition
8
Language
English
Total pages
768
Pub.-date
January 2020
ISBN13
9781292264769
ISBN
1292264764
Related Titles


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9781292264769
Introduction to Mathematical Statistics, Global Edition
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Description

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. 

Features

A comprehensive introduction to mathematical statistics with a proven approach

·    In-depth treatment of sufficiency and testing theory includes uniformly most powerful tests and likelihood ratio tests.

·    The text’s flexible organization makes it ideal for use with a range of mathematical statistics courses.

·    New - Many additional real data sets to illustrate statistical methods or compare methods. 

o The data sets are also available to students in the free R package hmcpkg. They can also be individually downloaded in an R session at https://media.pearsoncmg.com/intl/ge/abp/resources/products/product.html#product,isbn=9781292264769

o The R code for the analyses on these data sets are generally given in the text for the students’ benefit.

·    Revised - Expanded use of the statistical software R, a powerful statistical language which is free and can run on all three main platforms. However, instructors can choose another statistical package if desired.

o Use of R functions is increased to compute analyses and simulation studies, including several games. 

o A brief R primer in Appendix B suffices for the understanding of the R used in the text.

·    New - Downloadable, supplemented mathematical review material in Appendix A: reviews sequences, infinite series, differentiation, and integration (univariate and bivariate).

·    Revised - Expanded discussion of iterated integrals, with added figures to clarify discussion. 

·    New - A new subsection on the bivariate normal distribution begins the section on the multivariate normal distribution in Chapter 3 (Some Special Distributions). 

·    New - Several important topics have been added, including Tukey’s multiple comparison procedure in Chapter 9 (Inferences About Normal Linear Models)and confidence intervals for the correlation coefficients found in Chapters 9 and 10 (Nonparametric and Robust Statistics).

·    New - Discussion on standard errors for estimates obtained by bootstrapping the sample is now offered in Chapter 7 (Sufficiency).

·    Revised - Several topics that were discussed in the Exercises are now discussed in the text, including quantiles in Section 1.7.1 and hazard functions in Section 3.3.

Definitions, equations, and theorems are set in bold type help students study more effectively.

New to this Edition

·    Many additional real data sets to illustrate statistical methods or compare methods. 

o The data sets are also available to students in the free R package hmcpkg. They can also be individually downloaded in an R session at https://media.pearsoncmg.com/intl/ge/abp/resources/products/product.html#product,isbn=9781292264769

o The R code for the analyses on these data sets are generally given in the text for the students’ benefit.

·    Expanded use of the statistical software R, a powerful statistical language which is free and can run on all three main platforms. However, instructors can choose another statistical package if desired.

o Use of R functions is increased to compute analyses and simulation studies, including several games. 

o A brief R primer in Appendix B suffices for the understanding of the R used in the text.

·    Downloadable, supplemented mathematical review material in Appendix A: reviews sequences, infinite series, differentiation, and integration (univariate and bivariate).

·    Expanded discussion of iterated integrals, with added figures to clarify discussion. 

·    A new subsection on the bivariate normal distribution begins the section on the multivariate normal distribution in Chapter 3 (Some Special Distributions). 

·    Several important topics have been added, including Tukey’s multiple comparison procedure in Chapter 9 (Inferences About Normal Linear Models)and confidence intervals for the correlation coefficients found in Chapters 9 and 10 (Nonparametric and Robust Statistics).

·    Discussion on standard errors for estimates obtained by bootstrapping the sample is now offered in Chapter 7 (Sufficiency).

Several topics that were discussed in the Exercises are now discussed in the text, including quantiles in Section 1.7.1 and hazard functions in Section 3.3.

Table of Contents

 (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 

4.6 Additional Comments About Statistical Tests 

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*

10.6 Adaptive Procedures* 

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. Mathematical Comments

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

 

F. Answers to Selected Exercises

 

Index