Normal Approximation by Stein’s Method

  • Louis H.Y. Chen
  • Larry Goldstein
  • Qi-Man Shao
Part of the Probability and Its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 1-12
  3. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 13-44
  4. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 45-62
  5. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 63-145
  6. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 147-166
  7. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 167-220
  8. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 221-232
  9. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 233-244
  10. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 245-255
  11. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 257-291
  12. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 293-312
  13. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 313-341
  14. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 343-369
  15. Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao
    Pages 371-388
  16. Back Matter
    Pages 389-405

About this book

Introduction

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.

Keywords

60F05, 60B12, 62E17 Berry-Esseen bound, non-linear statistics Stein’s method exchangable pair, moderate deviations normal approximation, zero bias

Authors and affiliations

  • Louis H.Y. Chen
    • 1
  • Larry Goldstein
    • 2
  • Qi-Man Shao
    • 3
  1. 1., Mathematics DepartmentNational University of SingaporeSingaporeSingapore
  2. 2., Department of Mathematics KAP 108University of Southern CaliforniaLos AngelesUSA
  3. 3., Department of Mathematics and TechnologyHong Kong University of ScienceHong KongHong Kong/PR China

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-15007-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-15006-7
  • Online ISBN 978-3-642-15007-4
  • Series Print ISSN 1431-7028
  • About this book