A course in large sample theory

✍ Scribed by Ferguson, Thomas Shelburne

• Publisher: CRC Press
• Year: 2002
• Tongue: English
• Leaves: 258
• Series: Texts in statistical science
• Category: Library

✦ Synopsis

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.  Read more...

Abstract: 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

✦ Table of Contents

Content: Part 1 Basic Probability Theory / Thomas S. Ferguson --
chapter 1 Modes of Convergence / Thomas S. Ferguson --
chapter 2 Partial Converses to Theorem 1 / Thomas S. Ferguson --
chapter 3 Convergence in Law / Thomas S. Ferguson --
chapter 4 4 Laws of Large Numbers / Thomas S. Ferguson --
chapter 5 5 Central Limit Theorems / Thomas S. Ferguson --
part 2 Basic Statistical Large Sample Theory / Thomas S. Ferguson --
chapter 6 Slutsky Theorems / Thomas S. Ferguson --
chapter 7 Functions of the Sample Moments / Thomas S. Ferguson --
chapter 8 The Sample Correlation Coefficient / Thomas S. Ferguson --
chapter 9 Pearson{u2019}s Chi-Square / Thomas S. Ferguson --
chapter 10 Asymptotic Power of the Pearson Chi-Square Test / Thomas S. Ferguson --
part 3 Special Topics / Thomas S. Ferguson --
chapter 11 Stationary m-Dependent Sequences / Thomas S. Ferguson --
chapter 12 Some Rank Statistics / Thomas S. Ferguson --
chapter 13 Asymptotic Distribution of Sample Quantiles / Thomas S. Ferguson --
chapter 14 Asymptotic Theory of Extreme Order Statistics* / Thomas S. Ferguson --
chapter 15 Asymptotic Joint Distributions of Extrema / Thomas S. Ferguson --
part 4 Efficient Estimation and Testing / Thomas S. Ferguson --
chapter 16 A Uniform Strong Law of Large Numbers / Thomas S. Ferguson --
chapter 17 Strong Consistency of Maximum-Likelihood Estimates / Thomas S. Ferguson --
chapter 18 Asymptotic Normality of the Maximum-Likelihood Estimate / Thomas S. Ferguson --
chapter 19 The Cramér-Rao Lower Bound / Thomas S. Ferguson --
chapter 20 Asymptotic Efficiency / Thomas S. Ferguson --
chapter 21 Asymptotic Normality of Posterior Distributions / Thomas S. Ferguson --
chapter 22 Asymptotic Distribution of the Likelihood Ratio Test Statistic / Thomas S. Ferguson --
chapter 23 Minimum Chi-Square Estimates / Thomas S. Ferguson --
chapter 24 24 General Chi-Square Tests / Thomas S. Ferguson.

✦ Subjects

Sampling (Statistics);Asymptotic distribution (Probability theory);Law of large numbers.;Probability Theory.;Statistics.;MATHEMATICS / Applied.;MATHEMATICS / Probability & Statistics / General.