Normal Approximation by Steins Method by Louis H.Y. Chen (English) Paperback Boo

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Normal Approximation by Steins Method by Louis H.Y. Chen, Larry Goldstein, Qi-Man Shao

Since its introduction in 1972, Stein's method has offered a completely novel way of evaluating the quality of normal approximations.

FORMAT
Paperback LANGUAGE
English CONDITION
Brand New Publisher Description

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 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.

Back Cover

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.

Table of Contents

Preface.- .- of Stein's Method.- -Esseen Bounds for Independent Random Variables.- 4.L^1 Bounds.- 5.L^1 by Bounded Couplings.- 6 L^1: Applications.- -uniform Bounds for Independent Random Variables.- and Non-uniform Bounds under Local Dependence.- and Non-Uniform Bounds for Non-linear Statistics.- Deviations.- Normal Approximation.- normal approximation.- -normal Approximation.- .- References.- Author Index .- Subject Index.- Notation.

Review

From the reviews:"This book gives a complete and comprehensive overview of normal approximation using Stein's method. It serves both as an introductory textbook to graduate students who aim at becoming more familiar with Stein's method and as a research book taking into account the most recent advances in this area. … To conclude, the authors present in this book the foundations and the main developments of Stein's method … . The book is very pleasant to read and suitable for both graduate students and experienced researchers." (Anthony Réveillac, Mathematical Reviews, Issue 2012 b)

Review Quote

From the reviews: "This book gives a complete and comprehensive overview of normal approximation using Stein's method. It serves both as an introductory textbook to graduate students who aim at becoming more familiar with Stein's method and as a research book taking into account the most recent advances in this area. ... To conclude, the authors present in this book the foundations and the main developments of Stein's method ... . The book is very pleasant to read and suitable for both graduate students and experienced researchers." (Anthony Rveillac, Mathematical Reviews, Issue 2012 b)

Feature

First book that presents a complete self-contained treatment of Stein's methodIncludes many recent applicationsImportant reference for researchers and suitable for graduate student seminars

Details ISBN3642265650 Author Qi-Man Shao Short Title NORMAL APPROXIMATION BY STEIN Series Probability and Its Applications Language English ISBN-10 3642265650 ISBN-13 9783642265655 Media Book Format Paperback Birth 1940 Year 2012 Publication Date 2012-12-01 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany Pages 408 Edition 2011th DEWEY 510 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2011 ed. Alternative 9783642150067 Country of Origin NL Product Class Description Mathematics Illustrations 3 Illustrations, black and white Audience Educational: Primary & Secondary
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