A Course in Large Sample Theory

by Thomas S. Ferguson

Overview

A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.

Product Details

ISBN-13:	9781351470056
Publisher:	CRC Press
Publication date:	09/06/2017
Series:	Chapman & Hall/CRC Texts in Statistical Science
Sold by:	Barnes & Noble
Format:	eBook
Pages:	256
File size:	10 MB

About the Author

Thomas S. Ferguson

Table of Contents

Preface vii

Part 1 Basic Probability 1

1 Modes of Convergence 3

2 Partial Converses to Theorem 1 8

3 Convergence in Law 13

4 Laws of Large Numbers 19

5 Central Limit Theorems 26

Part 2 Basic Statistical Large Sample Theory 37

6 Slutsky Theorems 39

7 Functions of the Sample Moments 44

8 The Sample Correlation Coefficient 51

9 Pearson’s Chi-Square 56

10 Asymptotic Power of the Pearson Chi-Square Test 61

Part 3 Special Topics 67

11 Stationary m-Dependent Sequences 69

12 Some Rank Statistics 75

13 Asymptotic Distribution of Sample Quantiles 87

14 Asymptotic Theory of Extreme Order Statistics 94

15 Asymptotic Joint Distributions of Extrema 101

Part 4 Efficient Estimation and Testing 105

16 A Uniform Strong Law of Large Numbers 107

17 Strong Consistency of Maximum-Likelihood Estimates 112

18 Asymptotic Normality of the Maximum-Likelihood

Estimate 119

19 The Cram6r-Rao Lower Bound 126

20 Asymptotic Efficiency 133

21 Asymptotic Normality of Posterior Distributions 140

22 Asymptotic Distribution of the Likelihood Ratio

Test Statistic 144

23 Minimum Chi-Square Estimates 151

24 General Chi-Square Tests 163

Appendix: Solutions to the exercises 172

References 236

Index