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渐近统计(英文版)

  • 定价: ¥129
  • ISBN:9787519254025
  • 开 本:16开 平装
  • 作者:(荷)A.W.范德瓦特
  • 立即节省:
  • 2019-03-01 第1版
  • 2019-03-01 第1次印刷
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导语

  

内容提要

  

    A.W.范德瓦特著的《渐近统计(英文版)》是一部介绍渐近统计经典教材,内容实用而且数学理论论述严谨。书中除了介绍介绍渐近统计的核心内容——似然推断,M估计,渐近效率,U统计和秩过程,书中还涉及该领域的最新研究论题,如半参数模型,自助法,经验过程,等其他应用。本书各章有习题。

目录

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