●PREFACE TO THE 2015 EDITION
1 STATISTICAL MODELS,GOALS,AND PERFORMANCE CRITERIA
1.1 Data,Models,Parameters,and Statistics
1.1.1 Data and Models
1.1.2 Parametrizations and Parameters
1.1.3 Statistics as Functions on the Sample Space
1.1.4 Examples,Regression Models
1.2 Bayesian Models
1.3 The Decision Theoretic Framework
1.3.1 Components of the Decision Theory Framework
1.3.2 Comparison of Decision Procedures
1.3.3 Bayes and Minimax Criteria
1.4 Prediction
1.5 Sufficiency
1.6 Exponential Families
1.6.1 The One-Parameter Case
1.6.2 The ltiparameter Case
1.6.3 Building Exponential Families
1.6.4 Properties of Exponential Families
1.6.5 Conjugate Families of Prior Distributions
1.7 Problems and Complements
1.8 Notes
1.9 References
2 METHODS OF ESTIMATION
2.1 Basic Heuristics of Estimation
2.1.1 Minimum Contrast Estimates;Estimating Equations
2.1.2 The Plug-In and Extension Principles
2.2 Minimum Contrast Estimates and Estimating Equations
2.2.1 Least Squares and Weighted Least Squares
2.2.2 Maximum Likelihood
2.3 Maximum Likelihood in ltiparameter Exponential Families
2.4 Algorithmic Issues
2.4.1 The Method of Bisection
2.4.2 Coordinate Ascent
2.4.3 The Newton-Raphson Algorithm
2.4.4 The EM (Expectation/Maximization) Algorithm
2.5 Problems and Complements
2.6 Notes
2.7 References
3 MEASURES OF PERFORMANCE
3.1 Introduction
3.2 Bayes Procedures
3.3 Minimax Procedures
3.4 Unbiased Estimation and Risk Inequalities mi ianofT noiciosa or
3.4.1 Unbiased Estimation,Survey Sampling
3.4.2 The Information Inequality I soieiosT 1o moelnngmoD
3.5 Nondecision Theoretic Criteria
3.5.1 Computation
3.5.2 Interpretability
3.5.3 Robustness
3.6 Problems and Complements
3.7 Notes
3.8 References
4 TESTING AND CONFIDENCE REGIONS
4.1 Introduction
4.2 Choosing a Test Statistic: The Neyman-Pearson Lemma
4.3 Uniformly Most Powerful Tests and Monotone Likelihood Ratio Models
4.4 Confidence Bounds, Intervals, and Regions
4.5 The Duality Between Confidence Regions and Tests
4.6 Uniformly Most Accurate Confidence Bounds
4.7 Frequentist and Bayesian Formulations
4.8 Prediction Intervals
4.9 Likelihood Ratio Procedures
4.9.1 Introduction
4.9.2 Tests for the Mean of a Normal Distribution-Matched Pair Experi-ments
4.9.3 Tests and Confdence Intervals for the Difference in Means of Two Normal Populations
4.9.4 The Two-Sample Problem with Unequal Variances
4.9.5 Likelihood Ratio Procedures for Bivariate Normal Distributions
4.10 Problems and Complements
4.11 Notes
4.12 References
5 ASYMPTOTIC APPROXIMATIONS
5.1 Introduction:The Meaning and Uses of Asymptotics
5.2 Consistency
5.2.1 Plug-In Estimates and MLEs in Exponential Family Models
5.2.2 Consistency of Minimum Contrast Estimates
5.3 First-and Higher-Order Asymptotics:The Delta Method with Applications
5.3.1 The Delta Method for Moments
5.3.2 The Delta Method for In Law Approximations
5.3.3 Asymptotic Normality of the Maximum Likelihood Estimate in Exponential Families
5.4 Asymptotic Theory in One Dimension
5.4.1 Estimation:The ltinomial Case
5.4.2 Asymptotic Normality of Minimum Contrast and M-Estimates
5.4.3 Asymptotic Normality and Efficiency of the MLE
5.4.4 Testing
5.4.5 Confidence Bounds
5.5 Asymptotic Behavior and Optimality of the terior Distribution
5.6 Problems and Complements
5.7 Notes
5.8 References
6 INFERENCE IN THE MULTIPARAMETER CASE
6.1 Inference for Gaussian Linear Models
6.1.1 The Classical Gaussian Linear Model
6.1.2 Estimation
6.1.3 Tests and Confidence Intervals
6.2 Asymptotic Estimation Theory in p Dimensions
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