Normal Approximation by Stein's Method

 
 
Springer (Verlag)
  • erschienen am 1. Dezember 2012
 
  • Buch
  • |
  • Softcover
  • |
  • 420 Seiten
978-3-642-26565-5 (ISBN)
 
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.
Paperback
2011
  • Englisch
  • Heidelberg
  • |
  • Deutschland
Springer Berlin
  • Für Beruf und Forschung
  • |
  • Graduate
  • 3 s/w Abbildungen
  • |
  • 3 Illustrations, black and white; XII, 408 p. 3 illus.
  • Höhe: 235 mm
  • |
  • Breite: 155 mm
  • |
  • Dicke: 22 mm
  • 633 gr
978-3-642-26565-5 (9783642265655)
10.1007/978-3-642-15007-4
weitere Ausgaben werden ermittelt

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.

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.
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 Reveillac, Mathematical Reviews, Issue 2012 b)
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.

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