统计推断

出版说明 序 1 Probability Theory 1.1 Set Theory 1.2 Basics of Probability Theory 1.2.1 Axiomatic Foundations 1.2.2 The Calculus of Probabilities 1.2.3 Counting 1.2.4 Enumerating Outcomes 1.3 Conditional Probability and Independence 1.4 Random Variables 1.5 Distribution Functions 1.6 Density and Mass Functions 1.7 Exercises 1.8 Miscellanea 2 Transformations and Expectations 2.1 Distributions of Functions of a Random Variable 2.2 Expected Values 2.3 Moments and Moment Generating Functions 2.4 Differentiating Under an Integral Sign 2.5 Exercises 2.6 Miscellanea 3 Common Families of Distributions 3.1 Introduction 3.2 Discrete Distributions 3.3 Continuous Distributions 3.4 Exponential Families 3.5 Location and Scale Families 3.6 Inequalities and Identities 3.6.1 Probability Inequalities 3.6.2 Identities 3.7 Exercises 3.8 Miscellanea 4 Multiple Random Variables 4.1 Joint and Marginal Distributions 4.2 Conditional Distributions and Independence 4.3 Bivariate Transformations 4.4 Hierarchical Models and Mixture Distributions 4.5 Covariance and Correlation 4.6 Multivariate Distributions 4.7 Inequalities 4.7.1 Numerical Inequalities 4.7.2 Functional Inequalities 4.8 Exercises 4.9 Miscellanea 5 Properties of a Random Sample 5.1 Basic Concepts of Random Samples 5.2 Sums of Random Variables from a Random Sample 5.3 Sampling from the Normal Distribution 5.3.1 Properties of the Sample Mean and Variance 5.3.2 The Derived Distributions: Student's t and Snedecor's F 5.4 Order Statistics 5.5 Convergence Concepts 5.5.1 Convergence in Probability 5.5.2 Almost Sure Convergence 5.5.3 Convergence in Distribution 5.5.4 The Delta Method 5.6 Generating a Random Sample 5.6.1 Direct Methods 5.6.2 Indirect Methods 5.6.3 The Accept/Reject Algorithm 5.7 Exercises 5.8 Miscellanea 6 Principles of Data Reduction 6.1 Introduction 6.2 The Sufficiency Principle 6.2.1 Sufficient Statistics 6.2.2 Minimal Sufficient Statistics 6.2.3 Ancillary Statistics 6.2.4 Sufficient, Ancillary, and Complete Statistics …… 7 Point Estimation 8 Hypothesis Testing 8.1 Introduction 9 Interval Estimation 10 Asymptotic Evaluations 11 Analysis of Variance and Regression 12 Regression Models Appendix: Computer Algebra Table of Common Distributions References Author Index Subject Index

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