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����Distribution Theory
4��4 Normal One-Sample Problem����Estimation
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�� 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 ��2
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�� 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