# 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 i-xi
2. John E. Kolassa
Pages 1-4
3. John E. Kolassa
Pages 5-24
4. John E. Kolassa
Pages 25-57
5. John E. Kolassa
Pages 58-82
6. John E. Kolassa
Pages 83-95
7. John E. Kolassa
Pages 96-111
8. John E. Kolassa
Pages 112-131
9. John E. Kolassa
Pages 132-155
10. John E. Kolassa
Pages 156-165
11. John E. Kolassa
Pages 166-171
12. Back Matter
Pages 172-186

### 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 sub­ ject, 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 on 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

Calc boundary element method calculus character complex analysis computation distribution field form function functions likelihood maximum statistics theorem

#### Authors and affiliations

• John E. Kolassa
• 1
1. 1.Department of Biostatistics, School of Medicine and DentistryUniversity of RochesterRochesterUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-4277-0
• Copyright Information Springer-Verlag New York 1997
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-98224-3
• Online ISBN 978-1-4757-4277-0
• Series Print ISSN 0930-0325
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