Probability and Its Applications

Normal Approximation by Stein’s Method

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

  • 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
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eBook 49,99 €
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  • ISBN 978-3-642-15007-4
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Hardcover 62,35 €
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  • ISBN 978-3-642-15006-7
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  • Usually dispatched within 3 to 5 business days.
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Softcover 62,35 €
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  • ISBN 978-3-642-26565-5
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About this Textbook

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.

About the authors

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.

Reviews

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)

Table of contents (14 chapters)

  • Introduction

    Chen, Louis H. Y. (et al.)

    Pages 1-12

    Preview Buy Chapter 30,19 €
  • Fundamentals of Stein’s Method

    Chen, Louis H. Y. (et al.)

    Pages 13-44

    Preview Buy Chapter 30,19 €
  • Berry–Esseen Bounds for Independent Random Variables

    Chen, Louis H. Y. (et al.)

    Pages 45-62

    Preview Buy Chapter 30,19 €
  • L 1 Bounds

    Chen, Louis H. Y. (et al.)

    Pages 63-145

    Preview Buy Chapter 30,19 €
  • L ∞ by Bounded Couplings

    Chen, Louis H. Y. (et al.)

    Pages 147-166

    Preview Buy Chapter 30,19 €

Buy this book

eBook 49,99 €
price for Spain (gross)
  • ISBN 978-3-642-15007-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 62,35 €
price for Spain (gross)
  • ISBN 978-3-642-15006-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 62,35 €
price for Spain (gross)
  • ISBN 978-3-642-26565-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Normal Approximation by Stein’s Method
Authors
Series Title
Probability and Its Applications
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag GmbH Berlin Heidelberg
eBook ISBN
978-3-642-15007-4
DOI
10.1007/978-3-642-15007-4
Hardcover ISBN
978-3-642-15006-7
Softcover ISBN
978-3-642-26565-5
Series ISSN
1431-7028
Edition Number
1
Number of Pages
XII, 408
Number of Illustrations and Tables
3 b/w illustrations
Topics