Normal Approximation by Stein's Method / Edition 1 by Louis H.Y. Chen, Larry Goldstein, Qi-Man Shao | | 9783642150067 | Hardcover | Barnes & Noble
Normal Approximation by Stein's Method / Edition 1

Normal Approximation by Stein's Method / Edition 1

by Louis H.Y. Chen, Larry Goldstein, Qi-Man Shao
     
 

ISBN-10: 3642150063

ISBN-13: 9783642150067

Pub. Date: 10/27/2010

Publisher: Springer Berlin Heidelberg

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 dependence. Use of the method thus opens the door to the

Overview

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 dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology.
Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.

Product Details

ISBN-13:
9783642150067
Publisher:
Springer Berlin Heidelberg
Publication date:
10/27/2010
Series:
Probability and Its Applications Series
Edition description:
2011
Pages:
408
Product dimensions:
6.40(w) x 9.30(h) x 1.40(d)

Table of Contents

Preface.- 1.Introduction.- 2.Fundamentals of Stein's Method.- 3.Berry-Esseen Bounds for Independent Random Variables.- 4.Lsub1 Bounds.- 5.Lsub1 by Bounded Couplings.- 6 Lsub1: 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.

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