Normal Approximation by Stein¿s Method

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Beschreibung

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.

Über den Autor

Louis Chen's
research interests are in probability and computational biology, focusing largely on Stein's method. He is well-known for his pioneering work on Poisson approximation. He is an elected Fellow of the Institute of Mathematical Statistics and of the Academy of Sciences for the Developing World. He has also served as Associate Editor of Statistica Sinica and Bernoulli.

Larry Goldstein
has studied Stein's method since 1989, and is a noted researcher in the field. He was elected Fellow of the Institute of Mathematical Statistics in 2003, and serves on the editorial board of Bernoulli.

Qi-Man Shao
has been working on limit theory in probability and statistics, especially on self-normalized large and moderate deviations and Stein's method for normal and non-normal approximation. He is an invited speaker (45 minutes) at the International Congress of Mathematicians 2010. He is an elected Fellow of the Institute of Mathematical Statistics, and has served on the editorial board of The Annals of Statistics and The Annals of Applied Probability.

Zusammenfassung

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

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Medium:	Taschenbuch
Reihe:	Probability and Its Applications
Inhalt:	xii 408 S. 3 s/w Illustr. 408 p. 3 illus.
ISBN-13:	9783642265655
ISBN-10:	3642265650
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Chen, Louis H. Y. Shao, Qi-Man Goldstein, Larry
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Probability and Its Applications
Maße:	235 x 155 x 23 mm
Von/Mit:	Louis H. Y. Chen (u. a.)
Erscheinungsdatum:	01.12.2012
Gewicht:	0,633 kg

Artikel-ID: 106133521