大樣本理論基礎

內容簡介

《大樣本理論基礎（英文版）》在講述一階大樣本理論方面比較獨特，討論了大量的套用，包括密度估計、自助法和抽樣方法論的漸進。《大樣本理論基礎（英文版）》的內容比較基礎，適合統計專業的研究生和有兩年微積分背景的套用領域。每章末有針對本章每節的問題和練習，每節末都附有小結。

Preface

1 Mathematical Background

1.1 The concept of limit

1.2 Embedding sequences

1.3 Infinite series

1.4 Order relations and rates of convergence

1.5 Continuity

1.6 Distributions

1.7 Problems

2 Convergence in Probability and in Law

2.1 Convergence in probability

2.2 Applications

2.3 Convergence in law

2.4 The central limit theorem

2.5 Taylor's theorem and the delta method

2.6 Uniform convergence

2.7 The CLT for independent non-identical random variables

2.8 Central limit theorem for dependent variables

2.9 Problems

3 Performance of Statistical Tests

3.1 Critical values

3.2 Comparing two treatments

3.3 Power and sample size

3.4 Comparison of tests: Relative efficiency

3.5 Robustness

3.6 Problems

4 Estimation

4.1 Confidence intervals

4.2 Accuracy of point estimators

4.3 Comparing estimators

4.4 Sampling from a finite population

4.5 Problems

5 Multivariate Extensions

5.1 Convergence of multivariate distributions