內容簡介

本書是一部介紹漸近統計經典教材，內容實用而且數學理論論述嚴謹。書中除了介紹介紹漸近統計的核心內容似然推斷，M估計，漸近效率，U統計和秩過程，書中還涉及該領域的新研究論題，如半參數模型，自助法，經驗過程，等其他應用。本書各章有習題。

作者介紹

A. W. van der Vaart (A.W.范德瓦特,荷蘭)

有多部著作，本書是其代表作之一，還著有Weak Convergence and Empirical Processes: With Applications to Statistics。

Preface
Notation

1. Introduction
1.1. Approximate Statistical Procedures
1.2. Asymptotic Optimality Theory
1.3. Limitations
1.4. The Index n

2. Stochastic Convergence
2.1. Basic Theory
2.2. Stochastic o and O Symbols
2.3. Characteristic Functions
2.4. Almost-Sure Representations
2.5. Convergence of Moments
2.6. Convergence-Determining Classes
2.7. Law of the Iterated Logarithm
2.8. Lindeberg-Feller Theorem
2.9. Convergence in Total Variation
Problems

3. Delta Method
3.1. Basic Result
3.2. Variance-Stabilizing Transformations
3.3. Higher-Order Expansions
3.4. Uniform Delta Method
3.5. Moments
Problems

4. Moment Estimators
4.1. Method of Moments
4.2. Exponential Families
Problems

5. M- and Z-Estimators
5.1. Introduction
5.2. Consistency
5.3. Asymptotic Normality
5.4. Estimated Parameters
5.5. Maximum Likelihood Estimators
5.6. Classical Conditions
5.7. One-Step Estimators
5.8. Rates of Convergence
5.9. Argmax Theorem
Problems

6. Contiguity
6.1. Likelihood Ratios
6.2. Contiguity
Problems

7. Local Asymptotic Normality
7.1. Introduction
7.2. Expanding the Likelihood
7.3. Convergence to a Normal Experiment
7.4. Maximum Likelihood
7.5. Limit Distributions under Alternatives
7.6. Local Asymptotic Normality
Problems

8. Efficiency of Estimators
8.1. Asymptotic Concentration
8,2, Relative Efficiency
8.3. Lower Bound for Experiments
8.4. Estimating Normal Means
8.5. Convolution Theorem
8.6. Almost-Everywhere Convolution Theorem
8.7. Local Asymptotic Minimax Theorem
8.8. Shrinkage Estimators
8.9. Achieving the Bound
8.10. Large Deviations
Problems

9. Limits of Experiments
9.1. Introduction
9.2. Asymptotic Representation Theorem
9.3. Asymptotic Normality
9.4. Uniform Distribution
9.5. Pareto Distribution
9.6. Asymptotic Mixed Normality
9.7. Heuristics
Problems

10. Bayes Procedures
10.1. Introduction
10.2. Bernstein-von Mises Theorem
10.3. Point Estimators
10.4. Consistency
Problems

11. Projections
11.1. Projections
11.2. Conditional Expectation
11.3. Projection onto Sums
11.4. Hoeffding Decomposition
Problems

12. U-Statistics
12.1. One-Sample U-Statistics
12.2. Two-Sample U-statistics
12.3. Degenerate U-Statistics
Problems

13. Rank, Sign, and Permutation Statistics
13.1. Rank Statistics
13.2. Signed Rank Statistics
13.3. Rank Statistics for Independence
13.4. Rank Statistics under Alternatives
13.5. Permutation Tests
13.6. Rank Central Limit Theorem
Problems

14. Relative Efficiency of Tests
14.1. Asymptotic Power Functions
14.2. Consistency
14.3. Asymptotic Relative Efficiency
14.4. Other Relative Efficiencies
14.5. Rescaling Rates
Problems

15. Efficiency of Tests
15.1. Asymptotic Representation Theorem
15.2. Testing Normal Means
15.3. Local Asymptotic Normality
15.4. One-Sample Location
15.5. Two-Sample Problems
Problems

16. Likelihood Ratio Tests
16.1. Introduction
16.2. Taylor Expansion
16.3. Using Local Asymptotic Normality
16.4. Asymptotic Power Functions
16.5. Bartlett Correction
16.6. Bahadur Efficiency
Problems

17. Chi-Square Tests
17.1. Quadratic Forms in Normal Vectors
17.2. Pearson Statistic
17.3. Estimated Parameters
17.4. Testing Independence
17.5. Goodness-of-Fit Tests
17.6. Asymptotic Efficiency
Problems

18. Stochastic Convergence in Metric Spaces
18.1. Metric and Normed Spaces
18.2. Basic Properties
18.3. Bounded Stochastic Processes
Problems

19. Empirical Processes
19.1. Empirical Distribution Functions
19.2. Empirical Distributions
19.3. Goodness-of-Fit Statistics
19.4. Random Functions
19.5. Changing Classes
19.6. Maximal Inequalities
Problems

20. Functional Delta Method
20.1. yon Mises Calculus
20.2. Hadamard-Differentiable Functions
20.3. Some Examples
Problems

21. Quantiles and Order Statistics
21.1. Weak Consistency
21.2. Asymptotic Normality
21.3. Median Absolute Deviation
21.4. Extreme Values
Problems

22. L-Statistics
22.1. Introduction
22.2. Hajek Projection
22.3. Delta Method
22.4. L-Estimators for Location
Problems

23. Bootstrap
23.1. Introduction
23.2. Consistency
23.3. Higher-Order Correctness
Problems

24. Nonparametric Density Estimation
24.1 Introduction
24.2 Kernel Estimators
24.3 Rate Optimality
24.4 Estimating a Unimodal Density
Problems

25. Semiparametric Models
25.1 Introduction
25.2 Banach and Hilbert Spaces
25.3 Tangent Spaces and Information
25.4 Efficient Score Functions
25.5 Score and Information Operators
25.6 Testing
25.7 Efficiency and the Delta Method
25.8 Efficient Score Equations
25.9 General Estimating Equations
25.10 Maximum Likelihood Estimators
25.11 Approximately Least-Favorable Submodels
25.12 Likelihood Equations
Problems

References
Index

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