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