Normal Approximation by Stein’s Method

• Main Authors: Chen, Louis H.Y (Author), Goldstein, Larry (Author), Shao, Qi-Man (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Probability and Its Applications,
• Subjects: Mathematics.; Probabilities.; Probability Theory and Stochastic Processes.

Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated de...

Table of Contents:

• Preface
• 1.Introduction
• 2.Fundamentals of Stein's Method
• 3.Berry-Esseen Bounds for Independent Random Variables
• 4.L^1 Bounds
• 5.L^1 by Bounded Couplings
• 6 L^1: Applications
• 7.Non-uniform Bounds for Independent Random Variables
• 8.Uniform and Non-uniform Bounds under Local Dependence
• 9.Uniform and Non-Uniform Bounds for Non-linear Statistics
• 10.Moderate Deviations
• 11.Multivariate Normal Approximation
• 12.Discretized normal approximation
• 13.Non-normal Approximation
• 14.Extensions
• References
• Author Index
• Subject Index
• Notation.