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1 Probability and Measure
1£®1 Measures
1£®2 Integration
1£®3 Events£¬ Probabilities£¬ and Random Variables
1£®4 Null Sets
1£®5 Densities
1£®6 Expectation
1£®7 Random Vectors
1£®8 Covariance Matrices
1£®9 Product Measures and Independence
1£®10 Conditional Distributions
1£®11 Problems

2 Exponential Families
2£®1 Densities and Parameters
2£®2 Differential Identities
2£®3 Dominated Convergence
2£®4 Moments£¬ Cumulants£¬ and Generating Functions
2£®5 Problems

3 Risk£¬ Sufficiency£¬ Completeness£¬ and Ancillarity
3£®1 Models£¬ Estimators£¬ and Risk Functions
3£®2 Sufficient Statistics
3£®3 Factorization Theorem
3£®4 Minimal Sufficiency
3£®5 Completeness
3£®6 Convex Loss and the Rao-Blackwell Theorem
3£®7 Problems

4 Unbiased Estimation
4£®1 Minimum Variance Unbiased Estimators
4£®2 Second Thoughts About Bias
4£®3 Normal One-Sample Problem¡ª¡ªDistribution Theory
4£®4 Normal One-Sample Problem¡ª¡ªEstimation
4£®5 Variance Bounds and Information
4£®6 Variance Bounds in Higher Dimensions
4£®7 Problems

5 Curved Exponential Families
5£®1 Constrained Families
5£®2 Sequential Experiments
5£®3 Multinomial Distribution and Contingency Tables
5£®4 Problems

6 Conditional Distributions
6£®1 Joint and Marginal Densities
6£®2 Conditional Distributions
6£®3 Building Models
6£®4 Proof of the Factorization Theorem
6£®5 Problems

7 Bayesian Estimation
7£®1 Bayesian Models and the Main Result
7£®2 Examples
7£®3 Utility Theory
7£®4 Problems

8 Large-Sample Theory
8£®1 Convergence in Probability
8£®2 Convergence in Distribution
8£®3 Maximum Likelihood Estimation
8£®4 Medians and Percentiles
8£®5 Asymptotic Relative Efficiency
8£®6 Scales of Magnitude
8£®7 Almost Sure Convergence
8£®8 Problems

9 Estimating Equations and Maximum Likelihood
9£®1 Weak Law for Random Functions
9£®2 Consistency of the Maximum Likelihood Estimator
9£®3 Limiting Distribution for the MLE
9£®4 Confidence Intervals
9£®5 Asymptotic Confidence Intervals
9£®6 EM Algorithm£º Estimation from Incomplete Data
9£®7 Limiting Distributions in Higher Dimensions
9£®8 M-Estimators for a Location Parameter
9£®9 Models with Dependent Observations
9£®10 Problems

10 Equivariant Estimation
10£®1 Group Structure
10£®2 Estimation
10£®3 Problems

11 Empirical Bayes and Shrinkage Estimators
11£®1 Empirical Bayes Estimation
11£®2 Risk of the James-Stein Estimator
11£®3 Decision Theory
11£®4 Problems

12 Hypothesis Testing
12£®1 Test Functions£¬ Power£¬ and Significance
12£®2 Simple Versus Simple Testing
12£®3 Uniformly Most Powerful Tests
12£®4 Duality Between Testing and Interval Estimation
12£®5 Generalized Neyman-Pearson Lemma
12£®6 Two-Sided Hypotheses
12£®7 Unbiased Tests
12£®8 Problems

13 Optimal Tests in Higher Dimensions
13£®1 Marginal and Conditional Distributions
13£®2 UMP Unbiased Tests in Higher Dimensions
13£®3 Examples
13£®4 Problems

14 General Linear Model
14£®1 Canonical Form
14£®2 Estimation
14£®3 Gauss-Markov Theorem
14£®4 Estimating ¦Ò2
14£®5 Simple Linear Regression
14£®6 Noncentral F and Chi-Square Distributions
14£®7 Testing in the General Linear Model
14£®8 Simultaneous Confidence Intervals
14£®9 Problems

15 Bayesian Inference£º Modeling and Computation
15£®1 Hierarchical Models
15£®2 Bayesian Robustness
15£®3 Markov Chains
15£®4 Metropolis-Hastings Algorithm
15£®5 Gibbs Sampler
15£®6 Image Restoration
15£®7 Problems

16 Asymptotic Optimality
16£®1 Superefficiency
16£®2 Contiguity
16£®3 Local Asymptotic Normality
16£®4 Minimax Estimation of a Normal Mean
16£®5 Posterior Distributions
16£®6 Locally Asymptotically Minimax Estimation
16£®7 Problems

17 Large-Sample Theory for Likelihood Ratio Tests
17£®1 Generalized Likelihood Ratio Tests
17£®2 Asymptotic Distribution of 2 log A
17£®3 Examples
17£®4 Wald and Score Tests
17£®5 Problems

18 Nonparametric Regression
18£®1 Kernel Methods
18£®2 Hilbert Spaces
18£®3 Splines
18£®4 Density Estimation
18£®5 Problems

19 Bootstrap Methods
19£®1 Introduction
19£®2 Bias Reduction
19£®3 Parametric Bootstrap Confidence Intervals
19£®4 Nonparametric Accuracy for Averages
19£®5 Problems

20 Sequential Methods
20£®1 Fixed Width Confidence Intervals
20£®2 Stopping Times and Likelihoods
20£®3 Optimal Stopping
20£®4 Sequential Probability Ratio Test
20£®5 Sequential Design
20£®6 Problems
A Appendices
A£®1 Functions
A£®2 Topology and Continuity in Rn
A£®3 Vector Spaces and the Geometry of Rn
A£®4 Manifolds and Tangent Spaces
A£®5 Taylor Expansion for Functions of Several Variables
A£®6 Inverting a Partitioned Matrix
A£®7 Central Limit Theory
A£®7£®1 Characteristic Functions
A£®7£®2 Central Limit Theorem
A£®7£®3 Extensions
B Solutions
B£®1 Problems of Chapter 1
B£®2 Problems of Chapter 2
B£®3 Problems of Chapter 3
B£®4 Problems of Chapter 4
B£®5 Problems of Chapter 5
B£®6 Problems of Chapter 6
B£®7 Problems of Chapter 7
B£®8 Problems of Chapter 8
B£®9 Problems of Chapter 9
B£®10 Problems of Chapter 10
B£®11 Problems of Chapter 11
B£®12 Problems of Chapter 12
B£®13 Problems of Chapter 13
B£®14 Problems of Chapter 14
B£®17 Problems of Chapter 17
References
Index