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Series Approximation Methods in Statistics

  • Book
  • © 1994

Overview

Authors:
  1. John E. Kolassa

    1. Department of Biostatistics, University of Rochester, School of Medicine and Dentistry, Rochester, USA

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Part of the book series: Lecture Notes in Statistics (LNS, volume 88)

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Table of contents (10 chapters)

  1. Front Matter

    Pages N2-viii
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  2. Asymptotics in General

    • John E. Kolassa
    Pages 1-4

  3. Characteristic Functions and the Berry-Esseen Theorem

    • John E. Kolassa
    Pages 5-20

  4. Edgeworth Series

    • John E. Kolassa
    Pages 21-48

  5. Saddlepoint Series for Densities

    • John E. Kolassa
    Pages 49-69

  6. Saddlepoint Series for Distribution Functions

    • John E. Kolassa
    Pages 70-80

  7. Multivariate Expansions

    • John E. Kolassa
    Pages 81-94

  8. Conditional Distribution Approximations

    • John E. Kolassa
    Pages 95-111

  9. Applications to Likelihood Ratio and Maximum Likelihood Statistics

    • John E. Kolassa
    Pages 112-131

  10. Other Topics

    • John E. Kolassa
    Pages 132-137

  11. Computational Aids

    • John E. Kolassa
    Pages 138-142

  12. Back Matter

    Pages 143-153
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Keywords

About this book

This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field. In presenting expansion limit theorems I have drawn heavily 011 notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted.

Reviews

From the reviews of the third edition:

"This book provides several important theoretical results that are relevant to Edgeworth and saddlepoint approximation to distribution functions, as well as to densities, in a simple and concise manner. … The current edition showcases a rich and expanded list of references, exercises, and some applications. … Two of the nice features of this book are its uniformity in notation and special attention to regularity conditions." (Technometrics, Vol. 49 (2), 2007)

"This third edition features an expanded collection of references, exercises, and applications. Results have been reconfigured to adhere to a more conventional ‘theorem/proof’ format, which should make the material more tractable to some readers. Kolassa’s updated text should continue to serve as a valuable resource for interested students and researchers on saddlepoint methods and Edgeworth expansions." (Joseph Cavanaugh, Journal of the American Statistical Association, Vol. 102 (480), 2007)

Authors and Affiliations

  • Department of Biostatistics, University of Rochester, School of Medicine and Dentistry, Rochester, USA

    John E. Kolassa

About the author

John E. Kolassa is Assistant Professor of Biostatistics at the University of Rochester.

Bibliographic Information

  • Book Title: Series Approximation Methods in Statistics

  • Authors: John E. Kolassa

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4757-4275-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • eBook ISBN: 978-1-4757-4275-6Published: 17 April 2013

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VIII, 153

  • Number of Illustrations: 33 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes

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