Series Approximation Methods in Statistics

  • John E. Kolassa

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

Table of contents

  1. Front Matter
    Pages N2-viii
  2. John E. Kolassa
    Pages 1-4
  3. John E. Kolassa
    Pages 21-48
  4. John E. Kolassa
    Pages 49-69
  5. John E. Kolassa
    Pages 70-80
  6. John E. Kolassa
    Pages 81-94
  7. John E. Kolassa
    Pages 95-111
  8. John E. Kolassa
    Pages 132-137
  9. John E. Kolassa
    Pages 138-142
  10. Back Matter
    Pages 143-153

About this book

Introduction

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.

Keywords

Area approximation boundary element method development field graphs proof review statistics techniques theorem university

Authors and affiliations

  • John E. Kolassa
    • 1
  1. 1.Department of BiostatisticsUniversity of Rochester, School of Medicine and DentistryRochesterUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4275-6
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94277-3
  • Online ISBN 978-1-4757-4275-6
  • Series Print ISSN 0930-0325
  • About this book