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:	9781138445765
Publisher:	Taylor & Francis
Publication date:	08/21/2017
Series:	Chapman & Hall/CRC Texts in Statistical Science
Pages:	260
Product dimensions:	6.12(w) x 9.19(h) x (d)

Table of Contents

Preface viiPart 1 Basic Probability 11 Modes of Convergence 32 Partial Converses to Theorem 1 83 Convergence in Law 134 Laws of Large Numbers 195 Central Limit Theorems 26Part 2 Basic Statistical Large Sample Theory 376 Slutsky Theorems 397 Functions of the Sample Moments 448 The Sample Correlation Coefficient 519 Pearson’s Chi-Square 5610 Asymptotic Power of the Pearson Chi-Square Test 61Part 3 Special Topics 6711 Stationary m-Dependent Sequences 6912 Some Rank Statistics 7513 Asymptotic Distribution of Sample Quantiles 8714 Asymptotic Theory of Extreme Order Statistics 9415 Asymptotic Joint Distributions of Extrema 101Part 4 Efficient Estimation and Testing 10516 A Uniform Strong Law of Large Numbers 10717 Strong Consistency of Maximum-Likelihood Estimates 11218 Asymptotic Normality of the Maximum-LikelihoodEstimate 11919 The Cram6r-Rao Lower Bound 12620 Asymptotic Efficiency 13321 Asymptotic Normality of Posterior Distributions 14022 Asymptotic Distribution of the Likelihood RatioTest Statistic 14423 Minimum Chi-Square Estimates 15124 General Chi-Square Tests 163Appendix: Solutions to the exercises 172References 236Index