# Series Approximation Methods in Statistics

• John E. Kolassa
Book

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

1. Front Matter
Pages N2-viii
2. John E. Kolassa
Pages 1-4
3. John E. Kolassa
Pages 5-20
4. John E. Kolassa
Pages 21-48
5. John E. Kolassa
Pages 49-69
6. John E. Kolassa
Pages 70-80
7. John E. Kolassa
Pages 81-94
8. John E. Kolassa
Pages 95-111
9. John E. Kolassa
Pages 112-131
10. John E. Kolassa
Pages 132-137
11. John E. Kolassa
Pages 138-142
12. Back Matter
Pages 143-153

### 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
• Print ISBN 978-0-387-94277-3
• Online ISBN 978-1-4757-4275-6
• Series Print ISSN 0930-0325
• Buy this book on publisher's site
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