数理统计-第2版

preface to the first edition
preface to the second edition
chapter 1. probability theory
　1.1 probability spaces and random elements
　　1.1.1 a-fields and measures
　　1.1.2 measurable functions and distributions
　1.2 integration and differentiation
　　1.2.1 integration
　　1.2.2 radon-nikodym derivative
　1.3 distributions and their characteristics
　　1.3.1 distributions and probability densities
　　1.3.2 moments and moment inequalities
　　1.3.3 moment generating and characteristic functions
　1.4 conditional expectations
　　1.4.1 conditional expectations
　　1.4.2 independence
　　1.4.3 conditional distributions
　　1.4.4 markov chains and martingales
1.5 asymptotic theory
　　1.5.1 convergence modes and stochastic orders
　　1.5.2 weak convergence
　　1.5.3 convergence of transformations
　　1.5.4 the law of large numbers
　　1.5.5 the central limit theorem
　　1.5.6 edgeworth and cornish-fisher expansions
　1.6 exercises
chapter 2. fundamentals of statistics
　2.1 populations, samples, and models
　　2.1.1 populations and samples
　　2.1.2 parametric and nonparametric models
　　2.1.3 exponential and location-scale families
　2.2 statistics, sufficiency, and completeness
　　2.2.1 statistics and their distributions
　　2.2.2 sufficiency and minimal sufficiency
　　2.2.3 complete statistics
　2.3 statistical decision theory
　　2.3.1 decision rules, loss functions, and risks
　　2.3.2 admissibility and optimmity
　2.4 statistical inference
　　2.4.1 point estimators
　　2.4.2 hypothesis tests
　　2.4.3 confidence sets
　2.5 asymptotic criteria and inference
　　2.5.1 consistency
　　2.5.2 asymptotic bias, variance, and mse
　　2.5.3 asymptotic inference
　2.6 exercises
chapter 3. unbiased estimation
3.1 the umvue
　　3.1.1 sufficient and complete statistics
　　3.1.2 a necessary andsufficient condition
　　3.1.3 information inequality
　　3.1.4 asymptotic properties of umvue’s
3.2 u-statistics
　　3.2.1 some examples
　　3.2.2 variances of u-statistics
　　3.2.3 the projection method
　……
chapter 4. estimation in parametric models
chapter 5. estimation in nonparametric models
chapter 6. hypothesis tests
chapter 7. confidence sets
references
list of notation
list of abbreviations
index of definitions, main results, and examples
author index
subject index