Normal Approximation by Stein's Method
-7 %

Normal Approximation by Stein's Method

 Previously published in hardcover
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ISBN-13:
9783642265655
Einband:
Previously published in hardcover
Erscheinungsdatum:
01.12.2012
Seiten:
420
Autor:
Louis H. Y. Chen
Gewicht:
631 g
Format:
235x155x22 mm
Sprache:
Englisch
Beschreibung:

Stein's method has offered a completely novel way of evaluating the quality of normal approximations. This volume contains thorough coverage of the method's fundamentals. It includes a large number of recent developments in both theory and applications.
First book that presents a complete self-contained treatment of Stein's method
Includes many recent applications
Important reference for researchers and suitable for graduate student seminars
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.
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.