美国霍格编著的《数理统计学导论(英文版第7版)》是数理统计方面的一本经典教材，自1959年出版以来，广受读者好评，并被众多院校选为教材，如布朗大学、乔治华盛顿大学等。第7版延续了前几版的一贯风格，清晰而全面地阐述了数理统计的基本理论，并且为了让读者更好地理解数理统计，还提供了丰富的例子和一些重要的背景材料。与前几版相比，本版引入了最近新的数理统计发展成果，采用现在流行的R软件进行统计计算和推断。本书特色全面覆盖估计和检验中的经典统计推断过程。深入讨论充分性和检验理论，包括一致最大功效检验和似然比检验。提供丰富的实例和练习，便于读者理解和巩固相关知识。附录B中给出更多的R函数实例，帮助读者了解使用R进行统计计算与模拟。

Preface

1 Probability and Distributions

 1．1 Introduction

 1．2 Set Theory

 1．3 The Probability Set Function

 1．4 Conditional Probability and Independence

 1．5 Random Variables

 1．6 Discrete Random Variables

 1．6．1 nansformations

 1．7 Continuous Random Variables

1．7．1 naDSformations

 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

2．1．1Expectation

 2．2 nansformations：Bivariate Random Variables

 2．3 Conditional Distributions and Expectations

 2．4 The Correlation Coefficient

 2．5 Independent Random Variables

 2．6 Extension to Several Random Variables

2．6．1*Multivariate Variance-Covariance Matrix

 2．7 nansformations 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 Г，χ2，andβ Distributions

 3．4 The Normal Distribution

 3．4．1Contaminated Normals

 3．5 The Multivariate Normal Distribution

 3．5．1*Applications

 3．6 t-and F-Distributions

3．6．1 The t-distribution

3．6．2 The F-distribution

3．6．3 Student’S Theorem

 3．7 Mixture Distributions

4 Some Elementary Statistical Inferences

 4．1 Sampling and Statistics

4．1．1 Histogram Estimates of pmfs and pdfs

 4．2 Confidence Intervals

4．2．1Confidence Intervals for Difference in Means

4．2．2Confidence Interval for Difference in Proportions

 4．3 Confidence Intervals for Parameters of Discrete Distributions

 4．4 CIrder Statistics

 4．4．1Quantiles

 4．4．2Confidence Intervals for Quantiles

 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

 4．8．1 Accept-Reject Generation Algorithm

 4．9 Bootstrap Procedures

 4．9．1 Percentile Bootstrap Confidence Intervals

 4．9．2Bootstrap Testing Procedures

 4．10 *Tolerance Limits for Distributions

5 Consistency and Limiting Distributions

 5．1 Convergence in Probability

 5．2 Convergence in Distribution

5．2．1Bounded in Probability

5．2．2 △-Method

5．2．3 Moment Generating Function Technique

 5．3 Central Limit Theorem

 5．4 *Extensions to Multivariate Distributions

6 Maximum Likelihood Methods

 6．1 Maximum Likeli．hood Estimation

 6．2 Rao-Cram6r Lower Bound and E伍ciency

 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 Su伍cient 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 Cuse 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

 8．4 The Sequential Probability Ratio Test

 8．5Minimax and Classification Procedures

8．5．1 Minimax Procedures

8．5．2 Classification

9 Inferences About Normal MOdels

 9．1 Quadratic Forms

 9．2 One-Way ANOVA

 9．3 Noncentralχ2and F-Distributions

 9．4 Multiple Comparisons

 9．5 The Analysis of Variance

 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 Forills

10 Nonparametric and Robust Statistics

 10．1 Location Models

 10．2 Sample Median and the Sign Test

 10．2．1 Asymptotic Relative Efficiency

 10．2．2 Estimating Equations Based on the Sign Test

 10．2．3 Confidence Interval for the Median

 10．3 Signed-Rank Wilcoxon

10．3．1 Asymptotic Relative Emciency

10．3．2 Estimating Equations Based on Signed-Rank Wilcoxon

10．3．3 Confidence Interval for the Median

 10．4 Mann-Whitnev-Wilcoxon Procedure

10．4．1 Asymptotic Relative Efficiency

10．4．2 Estimating Equations Based on the Mann-Whitney-Wilcoxon

10．4．3 Confidence Interval for the Shift Parameter △

 10．5 General Rank Scores

10．5．1 Efficacy

10．5．2 Estimating Equations Based on General Scores

10．5．3 0ptimization：Best Estimates

 10．6 Adaptive Procedures

 10．7 Simple Linear Model

 10．8 Measures of Association

10．8．1 Kendall’S т

10．8．2 Spearman’S Rho

 10．9 Robust Concepts

10．9．1 Location Model

10．9．2 Linear Model

11 Bayesian Statistics

 11．1 Subjective Probability

 11．2 Bayesian Procedures

11．2．1 Prior and Posterior Distributions

11．2．2 Bayesian Point Estimation

11．2．3 Bayesian Interval Estimation

11．2．4 Bayesian Testing Procedures

11．2．5 Bayesian Sequential Procedures

 11．3 More Bayesian Terminology and Ideas

 11．4 Gibbs Sampler

 11．5 Modern Bayesian Methods

11．5．1 Empirical Bayes

A Mathematical Comments

 A．1 Regularity Conditions

 A．2 Sequences

B R Functions

C Tables of Distributions

D Lists of Common Distributions

E References

F Answers to Selected Exercisds

 Index