Introduction to Mathematical Statistics, 8th Edition, By Allen Craig, Robert Hogg, Joseph McKean (eBook PDF)

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Introduction to Mathematical Statistics Contents Preface Content and Course Planning Chapter 1 Probability and Distributions 1.1 Introduction 1.2 Sets 1.2.1 Review of Set Theory 1.2.2 Set Func... tions Exercises 1.3 The Probability Set Function 1.3.1 Counting Rules 1.3.2 Additional Properties of Probability Exercises 1.4 Conditional Probability and Independence 1.4.1 Independence 1.4.2 Simulations Exercises 1.5 Random Variables Exercises 1.6 Discrete Random Variables 1.6.1 Transformations Exercises 1.7 Continuous Random Variables 1.7.1 Quantiles 1.7.2 Transformations 1.7.3 Mixtures of Discrete and Continuous Type Distributions Exercises 1.8 Expectation of a Random Variable 1.8.1 R Computation for an Estimation of the Expected Gain Exercises 1.9 Some Special Expectations Exercises 1.10 Important Inequalities Exercises Chapter 2 Multivariate Distributions 2.1 Distributions of Two Random Variables 2.1.1 Marginal Distributions 2.1.2 Expectation Exercises 2.2 Transformations: Bivariate Random Variables Exercises 2.3 Conditional Distributions and Expectations Exercises 2.4 Independent Random Variables Exercises 2.5 The Correlation Coefficient Exercises 2.6 Extension to Several Random Variables 2.6.1 *Multivariate Variance-Covariance Matrix Exercises 2.7 Transformations for Several Random Variables Exercises 2.8 Linear Combinations of Random Variables Exercises Chapter 3 Some Special Distributions 3.1 The Binomial and Related Distributions 3.1.1 Negative Binomial and Geometric Distributions 3.1.2 Multinomial Distribution 3.1.3 Hypergeometric Distribution Exercises 3.2 The Poisson Distribution Exercises 3.3 The Γ, χ2, and β Distributions 3.3.1 The χ2-Distribution 3.3.2 The β-Distribution Exercises 3.4 The Normal Distribution 3.4.1 *Contaminated Normals Exercises 3.5 The Multivariate Normal Distribution 3.5.1 Bivariate Normal Distribution 3.5.2 *Multivariate Normal Distribution, General Case 3.5.3 *Applications Exercises 3.6 t- and F-Distributions 3.6.1 The t-distribution 3.6.2 The F-distribution 3.6.3 Student’s Theorem Exercises 3.7 *Mixture Distributions Exercises Chapter 4 Some Elementary Statistical Inferences 4.1 Sampling and Statistics 4.1.1 Point Estimators 4.1.2 Histogram Estimates of pmfs and pdfs The distribution of X is discrete The Distribution of X Is Continuous Exercises 4.2 Confidence Intervals 4.2.1 Confidence Intervals for Difference in Means 4.2.2 Confidence Interval for Difference in Proportions Exercises 4.3 *Confidence Intervals for Parameters of Discrete Distributions Numerical Illustration Numerical Illustration Exercises 4.4 Order Statistics 4.4.1 Quantiles 4.4.2 Confidence Intervals for Quantiles Exercises 4.5 Introduction to Hypothesis Testing Exercises 4.6 Additional Comments About Statistical Tests 4.6.1 Observed Significance Level, p-value Exercises 4.7 Chi-Square Tests Exercises 4.8 The Method of Monte Carlo 4.8.1 Accept–Reject Generation Algorithm Exercises 4.9 Bootstrap Procedures 4.9.1 Percentile Bootstrap Confidence Intervals 4.9.2 Bootstrap testing procedures Exercises 4.10 *Tolerance Limits for Distributions Exercises Chapter 5 Consistency and Limiting Distributions 5.1 Convergence in Probability 5.1.1 Sampling and Statistics Exercises 5.2 Convergence in Distribution 5.2.1 Bounded in Probability 5.2.2 ∆-Method 5.2.3 Moment Generating Function Technique Exercises 5.3 Central Limit Theorem Exercises 5.4 *Extensions to Multivariate Distributions Exercises Chapter 6 Maximum Likelihood Methods 6.1 Maximum Likelihood Estimation Exercises 6.2 Rao–Cramér Lower Bound and Efficiency Exercises 6.3 Maximum Likelihood Tests Exercises 6.4 Multiparameter Case: Estimation Exercises 6.5 Multiparameter Case: Testing Exercises 6.6 The EM Algorithm Exercises Chapter 7 Sufficiency 7.1 Measures of Quality of Estimators Exercises 7.2 A Sufficient Statistic for a Parameter Exercises 7.3 Properties of a Sufficient Statistic Exercises 7.4 Completeness and Uniqueness Exercises 7.5 The Exponential Class of Distributions Exercises 7.6 Functions of a Parameter 7.6.1 Bootstrap Standard Errors Exercises 7.7 The Case of Several Parameters Exercises 7.8 Minimal Sufficiency and Ancillary Statistics Exercises 7.9 Sufficiency, Completeness, and Independence Exercises Chapter 8 Optimal Tests of Hypotheses 8.1 Most Powerful Tests Exercises 8.2 Uniformly Most Powerful Tests Exercises 8.3 Likelihood Ratio Tests 8.3.1 Likelihood Ratio Tests for Testing Means of Normal Distributions 8.3.2 Likelihood Ratio Tests for Testing Variances of Normal Distributions Exercises 8.4 *The Sequential Probability Ratio Test Exercises 8.5 *Minimax and Classification Procedures 8.5.1 Minimax Procedures 8.5.2 Classification Exercises Chapter 9 Inferences About Normal Linear Models 9.1 Introduction 9.2 One-Way ANOVA Exercises 9.3 Noncentral χ2 and F-Distributions Exercises 9.4 Multiple Comparisons 9.5 Two-Way ANOVA 9.5.1 Interaction between Factors Exercises 9.6 A Regression Problem 9.6.1 Maximum Likelihood Estimates 9.6.2 *Geometry of the Least Squares Fit Exercises 9.7 A Test of Independence Exercises 9.8 The Distributions of Certain Quadratic Forms Exercises 9.9 The Independence of Certain Quadratic Forms Exercises Chapter 10 Nonparametric and Robust Statistics 10.1 Location Models Exercises 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 Exercises 10.3 Signed-Rank Wilcoxon 10.3.1 Asymptotic Relative Efficiency 10.3.2 Estimating Equations Based on Signed-Rank Wilcoxon 10.3.3 Confidence Interval for the Median 10.3.4 Monte Carlo Investigation Exercises 10.4 Mann–Whitney–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 Δ 10.4.4 Monte Carlo Investigation of Power Exercises 10.5 * General Rank Scores 10.5.1 Efficacy 10.5.2 Estimating Equations Based on General Scores 10.5.3 Optimization: Best Estimates Exercises 10.6 *Adaptive Procedures Exercises 10.7 Simple Linear Model Exercises 10.8 Measures of Association 10.8.1 Kendall’s τ 10.8.2 Spearman’s Rho Exercises 10.9 Robust Concepts 10.9.1 Location Model Influence Functions Breakdown Point of an Estimator 10.9.2 Linear Model Least Squares and Wilcoxon Procedures Influence Functions Breakdown Points Intercept Exercises Endnotes Chapter 11 Bayesian statistics 11.1 Bayesian Procedures 11.1.1 Prior and Posterior Distributions 11.1.2 Bayesian Point Estimation 11.1.3 Bayesian Interval Estimation 11.1.4 Bayesian Testing Procedures 11.1.5 Bayesian Sequential Procedures Exercises 11.2 More Bayesian Terminology and Ideas Exercises 11.3 Gibbs sampler Exercises 11.4 Modern bayesian methods 11.4.1 Empirical bayes Exercises Appendix A Mathematical Comments A.1 Regularity Conditions A.2 Sequences Exercises Appendix 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 Appendix C Lists of Common Distributions Appendix D Tables of Distributions Table I Chi-Square Distribution Table II Normal Distribution Table III t-Distribution Table IV F-Distribution Upper 0.05 Critical Points Table IV F-Distribution, Continued Upper 0.05 Critical Points Table IV F-Distribution, Continued Upper 0.01 Critical Points Table IV F-Distribution, Continued Upper 0.01 Critical Points Appendix E References Appendix F Answers to Selected Exercises Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Index [Show More]

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