A Course in Large Sample Theory

by Ferguson,Thomas S.

• ISBN13: 9780412043710
• ISBN10: 0412043718
• Format: Paperback
• Copyright: 1996-07-01
• Publisher: Chapman & Hall/

Summary

Presented in four parts, this book provides a complete picture of genome statistics. 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 ideal for 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, making it an ideal text for self study.

Table of Contents

Preface
Basic Probability	p. 1
Modes of Convergence	p. 3
Partial Converses to Theorem 1	p. 8
Convergence in Law	p. 13
Laws of Large Numbers	p. 19
Central Limit Theorems	p. 26
Basic Statistical Large Sample Theory	p. 37
Slutsky Theorems	p. 39
Functions of the Sample Moments	p. 44
The Sample Correlation Coefficient	p. 51
Pearson's Chi-Square	p. 56
Asymptotic Power of the Pearson Chi-Square Test	p. 61
Special Topics	p. 67
Stationary m-Dependent Sequences	p. 69
Some Rank Statistics	p. 75
Asymptotic Distribution of Sample Quantiles	p. 87
Asymptotic Theory of Extreme Order Statistics	p. 94
Asymptotic Joint Distributions of Extrema	p. 101
Efficient Estimation and Testing	p. 105
A Uniform Strong Law of Large Numbers	p. 107
Strong Consistency of Maximum-Likelihood Estimates	p. 112
Asymptotic Normality of the Maximum-Likelihood Estimate	p. 119
The Cramer-Rao Lower Bound	p. 126
Asymptotic Efficiency	p. 133
Asymptotic Normality of Posterior Distributions	p. 140
Asymptotic Distribution of the Likelihood Ratio Test Statistic	p. 144
Minimum Chi-Square Estimates	p. 151
General Chi-Square Tests	p. 153
Appendix: Solutions to the exercises	p. 172
References	p. 236
Index	p. 239
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