目錄
PREFACE TO THE 2016 EDITION
I INTRODUCTION AND EXAMPLES
I.0 Basic Ideas and Conventions
I.1 Tests of Goodness of Fit and the Brownian Bridge
I.2 Testing Goodness of Fit to Parametric Hypotheses
I.3 Regular Parameters.Minimum Distance Estimates
I.4 Permutation Tests
I.5 Estimation of Irregular Parameters
1.6 Stein and Empirical Bayes Estimation
I.7 Model Selection
I.8 Problems and Complements
I.9 Notes
7 TOOLS FOR ASYMPTOTIC ANALYSIS
7.1 Weak Convergence in Function Spaces
7.1.1 Stochastic Processes and Weak Convergence
7.1.2 Maximal Inequalities
7.1.3 Empirical Processes on Function Spaces
7.2 The Delta Method in Infinite Dimensional Space
7.2.1 Influence Functions.The Gateaux and Frechet Derivatives
7.2.2 The Quantile Process
17.3 Further Expansions
7.3.1 The von Mises Expansion
7.3.2 The Hoeffding and Analysis of Variance Expansions
7.4 Problems and Complements
7.5 Notes
8 BUSTRIBUTION-FREE,UNBIASED,AND EOUIVARIANT PROCEDURES
8.1 Introduction
8.2 Similarity and Completenes
8.2.1 Testing
8.2.2 Testing Optimality Theory
8.2.3 Estimation
8.3 Invariance, Equivariance,and Minimax Procedures
8.3.1 Group Models
8.3.2 Group Models and Decision Theory
8.3.3 Characterizing Invariant Tests
8.3.4 Characterizing Equivariant Estimates
8.3.5 Minimaxity for Tests:Application to Group Models
8.3.6 Minimax Estimation,Admissibility,and Steinian Shrinkage
8.4 Problems and Complements
8.5 Notes
9 INFERENCE IN SEMIPARAMETRIC MODELS
9.1 Estimation in Semiparametric Models
9.1.1 Selected Examples
9.1.2 Regularization.Modified Maximum Likelihood
9.1.3 Other Modified and Approximate Likelihoods
9.1.4 Sieves and Regularization
9.2 Asymptotics.Consistency and Asymptotic Normality
9.2.1 A General Consistency Criterion
9.2.2 Asymptotics for Selected Models
9.3 Efficiency in Semiparametric Models
9.4 Tests and Empirical Process Theory
9.5 Asymptotic Properties of Likelihoods.Contiguity
9.6 Problems and Complements
9.7 Notes
10 MONTE CARLO METHODS
10.1 The Nature of Monte Carlo Methods
10.2 Three Basic Monte Carlo Metheds
10.2.1 Simple Monte Carlo
10.2.2 Importance Sampling
10.2.3 Rejective Sampling
10.3 The Bootstrap
10.3.1 Bootstrap Samples and Bias Corections
10.3.2 Bootstrap Variance and Confidence Bounds
10.3.3 The General i.i.d.Nonparametric Bootstrap
10.3.4 Asymptotic Theory for the Bootstrap
10.3.5 Examples Where Efron's Bootstrap Fails.The m out of n Bootstraps
10.4 Markov Chain Monte Carlo
10.4.1 The Basic MCMC Framework
10.4.2 Metropolis Sampling Algorithms
10.4.3 The Gibbs Samplers
10.4.4 Sped of Convergence and Eficiency of MCMC
10.5 Applications of MCMC to Bayesian and Frequentist Interence
10.6 Problems and Complements
10.7 Notes
11 NONPARAMETRIC INFERENCE FOR FUNCTIONS OF ONE VARIABLE
11.1 Introduction
11.2 Convolution Kernel Estimates on R
11.2.1 Uniform Local Behavior of Kernel Density Estimates
11.2.2 Global Behavior of Convolution Kernel Estimates
11.2.3 Performance and Bandwidth Choice
11.2.4 Discussion of Convolution Kernel Estimates
11.3 Minimum Contrast Estimates:Reducing Boundary Bias
11.4 Regularization and Nonlinear Density Estimates
11.4.1 Regularization and Roughness Penalties
11.4.2 Sieves.Machine Learning.Log Density Estimation
11.4.3 Nearest Neighbor Density Estimates
11.5 Confidence Regions
11.6 Nonparametric Regression for One Covariate
11.6.1 Estimation Principles
11.6.2 Asymptotic Bias and Variance Calculations
11.7 Problems and Complements
12 PREDICTION AND MACHINE LEARNING
12.1 Introduction
12.1.1 Statistical Approaches to Modeling and Analyzing Multidimen-sional data.Sieves
12.1.2 Machine Learning Approaches
12.1.3 Outline
12.2 Classification and Prediction
12.2.1 Multivariate Density and Regression Estimation
12.2.2 Bayes Rule and Nonparametric Classification
12.2.3 Sieve Methods
12.2.4 Machine Learning Approaches
12.3 Asymptotic Risk Criteria
12.3.1 Optimal Prediction in Parametric Regression Models
12.3.2 Optimal Rates of Convergence for Estimation and Prediction in Nonparametric Models
12.3.3 The Gaussian White Noise (GWN) Model
12.3.4 Minimax Bounds on IMSE for Subsets of the GWN Model
12.3.5 Sparse Submodels
12.4 Oracle Inequalities
12.4.1 Stein's Unbiased Risk Estimate
12.4.2 Oracle Inequality for Shrinkage Estimators
12.4.3 Oracle Inequality and Adaptive Minimax Rate for Truncated Esti-mates
12.4.4 An Oracle Inequality for Classification
12.5 Performance and Tuning via Cross Validation
12.5.1 Cross Validation for Tuning Parameter Choice
12.5.2 Cross Validation for Measuring Performance
12.6 Model Selection and Dimension Reduction
12.6.1 A Bayesian Criterion for Model Selection
12.6.2 Inference after Model Selection
12.6.3 Dimension Reduction via Principal Component Analysis
12.7 Topics Briefly Touched and Current Frontiers
12.8 Problems and Complements
D APPENDIX D.SUPPLEMENTS TO TEXT
D.1 Probability Results
D.8 Problems and Complements
E SOLUTIONS FOR VOLUME II
REFERENCES
SUBJECT INDEX
AUTHOR INDEX
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