Statistical Inference Second Edition2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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1 Probability Theory1

1.1 Set Theory1

1.2 Basics of Probability Theory5

1.2.1 Axiomatic Foundations5

1.2.2 The Calculus of Probabilities9

1.2.3 Counting13

1.2.4 Enumerating Outcomes16

1.3 Conditional Probability and Independence20

1.4 Random Variables27

1.5 Distribution Functions29

1.6 Density and Mass Functions34

1.7 Exercises37

1.8 Miscellanea44

2 Transformations and Expectations47

2.1 Distributions of Functions of a Random Variable47

2.2 Expected Values55

2.3 Moments and Moment Generating Functions59

2.4 Differentiating Under an Integral Sign68

2.5 Exercises76

2.6 Miscellanea82

3 Common Families of Distributions85

3.1 Introduction85

3.2 Discrete Distributions85

3.3 Continuous Distributions98

3.4 Exponential Families111

3.5 Location and Scale Families116

3.6 Inequalities and Identities121

3.6.1 Probability Inequalities122

3.6.2 Identities123

3.7 Exercises127

3.8 Miscellanea135

4 Multiple Random Variables139

4.1 Joint and Marginal Distributions139

4.2 Conditional Distributions and Independence147

4.3 Bivariate Transformations156

4.4 Hierarchical Models and Mixture Distributions162

4.5 Covariance and Correlation169

4.6 Multivariate Distributions177

4.7 Inequalities186

4.7.1 Numerical Inequalities186

4.7.2 Functional Inequalities189

4.8 Exercises192

4.9 Miscellanea203

5 Properties of a Random Sample207

5.1 Basic Concepts of Random Samples207

5.2 Sums of Random Variables from a Random Sample211

5.3 Sampling from the Normal Distribution218

5.3.1 Properties of the Sample Mean and Variance218

5.3.2 The Derived Distributions: Student's t and Snedecor's F222

5.4 Order Statistics226

5.5 Convergence Concepts232

5.5.1 Convergence in Probability232

5.5.2 Almost Sure Convergence234

5.5.3 Convergence in Distribution235

5.5.4 The Delta Method240

5.6 Generating a Random Sample245

5.6.1 Direct Methods247

5.6.2 Indirect Methods251

5.6.3 The Accept/Reject Algorithm253

5.7 Exercises255

5.8 Miscellanea267

6 Principles of Data Reduction271

6.1 Introduction271

6.2 The Sufficiency Principle272

6.2.1 Sufficient Statistics272

6.2.2 Minimal Sufficient Statistics279

6.2.3 Ancillary Statistics282

6.2.4 Sufficient, Ancillary, and Complete Statistics284

6.3 The Likelihood Principle290

6.3.1 The Likelihood Function290

6.3.2 The Formal Likelihood Principle292

6.4 The Equivariance Principle296

6.5 Exercises300

6.6 Miscellanea307

7 Point Estimation311

7.1 Introduction311

7.2 Methods of Finding Estimators312

7.2.1 Method of Moments312

7.2.2 Maximum Likelihood Estimators315

7.2.3 Bayes Estimators324

7.2.4 The EM Algorithm326

7.3 Methods of Evaluating Estimators330

7.3.1 Mean Squared Error330

7.3.2 Best Unbiased Estimators334

7.3.3 Sufficiency and Unbiasedness342

7.3.4 Loss Function Optimality348

7.4 Exercises355

7.5 Miscellanea367

8 Hypothesis Testing373

8.1 Introduction373

8.2 Methods of Finding Tests374

8.2.1 Likelihood Ratio Tests374

8.2.2 Bayesian Tests379

8.2.3 Union-Intersection and Intersection-Union Tests380

8.3 Methods of Evaluating Tests382

8.3.1 Error Probabilities and the Power Function382

8.3.2 Most Powerful Tests387

8.3.3 Sizes of Union-Intersection and Intersection-Union Tests394

8.3.4 p-Values397

8.3.5 Loss Function Optimality400

8.4 Exercises402

8.5 Miscellanea413

9 Interval Estimation417

9.1 Introduction417

9.2 Methods of Finding Interval Estimators420

9.2.1 Inverting a Test Statistic420

9.2.2 Pivotal Quantities427

9.2.3 Pivoting the CDF430

9.2.4 Bayesian Intervals435

9.3 Methods of Evaluating Interval Estimators440

9.3.1 Size and Coverage Probability440

9.3.2 Test-Related Optimality444

9.3.3 Bayesian Optimality447

9.3.4 Loss Function Optimality449

9.4 Exercises451

9.5 Miscellanea463

10 Asymptotic Evaluations467

10.1 Point Estimation467

10.1.1 Consistency467

10.1.2 Efficiency470

10.1.3 Calculations and Comparisons473

10.1.4 Bootstrap Standard Errors478

10.2 Robustness481

10.2.1 The Mean and the Median482

10.2.2 M-Estimators484

10.3 Hypothesis Testing488

10.3.1 Asymptotic Distribution of LRTs488

10.3.2 Other Large-Sample Tests492

10.4 Interval Estimation496

10.4.1 Approximate Maximum Likelihood Intervals496

10.4.2 Other Large-Sample Intervals499

10.5 Exercises504

10.6 Miscellanea515

11 Analysis of Variance and Regression521

11.1 Introduction521

11.2 Oneway Analysis of Variance522

11.2.1 Model and Distribution Assumptions524

11.2.2 The Classic ANOVA Hypothesis525

11.2.3 Inferences Regarding Linear Combinations of Means527

11.2.4 The ANOVA F Test530

11.2.5 Simultaneous Estimation of Contrasts534

11.2.6 Partitioning Sums of Squares536

11.3 Simple Linear Regression539

11.3.1 Least Squares: A Mathematical Solution542

11.3.2 Best Linear Unbiased Estimators: A Statistical Solution544

11.3.3 Models and Distribution Assumptions548

11.3.4 Estimation and Testing with Normal Errors550

11.3.5 Estimation and Prediction at a Specified x = x0557

11.3.6 Simultaneous Estimation and Confidence Bands559

11.4 Exercises563

11.5 Miscellanea572

12 Regression Models577

12.1 Introduction577

12.2 Regression with Errors in Variables577

12.2.1 Functional and Structural Relationships579

12.2.2 A Least Squares Solution581

12.2.3 Maximum Likelihood Estimation583

12.2.4 Confidence Sets588

12.3 Logistic Regression591

12.3.1 The Model591

12.3.2 Estimation593

12.4 Robust Regression597

12.5 Exercises602

12.6 Miscellanea608

Appendix: Computer Algebra613

Table of Common Distributions621

References629

Author Index645

Subject Index649