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A Course in Large Sample Theory,9780412043710

A Course in Large Sample Theory

Format: Paperback
Pub. Date: 7/1/1996
Publisher(s): Chapman & Hall/


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

Basic Probabilityp. 1
Modes of Convergencep. 3
Partial Converses to Theorem 1p. 8
Convergence in Lawp. 13
Laws of Large Numbersp. 19
Central Limit Theoremsp. 26
Basic Statistical Large Sample Theoryp. 37
Slutsky Theoremsp. 39
Functions of the Sample Momentsp. 44
The Sample Correlation Coefficientp. 51
Pearson's Chi-Squarep. 56
Asymptotic Power of the Pearson Chi-Square Testp. 61
Special Topicsp. 67
Stationary m-Dependent Sequencesp. 69
Some Rank Statisticsp. 75
Asymptotic Distribution of Sample Quantilesp. 87
Asymptotic Theory of Extreme Order Statisticsp. 94
Asymptotic Joint Distributions of Extremap. 101
Efficient Estimation and Testingp. 105
A Uniform Strong Law of Large Numbersp. 107
Strong Consistency of Maximum-Likelihood Estimatesp. 112
Asymptotic Normality of the Maximum-Likelihood Estimatep. 119
The Cramer-Rao Lower Boundp. 126
Asymptotic Efficiencyp. 133
Asymptotic Normality of Posterior Distributionsp. 140
Asymptotic Distribution of the Likelihood Ratio Test Statisticp. 144
Minimum Chi-Square Estimatesp. 151
General Chi-Square Testsp. 153
Appendix: Solutions to the exercisesp. 172
Referencesp. 236
Indexp. 239
Table of Contents provided by Blackwell. All Rights Reserved.

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