Series Approximation Methods in Statistics

John E Kolassa

ISBN 10: 0387314091 / ISBN 13: 9780387314099

Published by Springer New York Apr 2006, 2006

About this Item

Neuware - 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 s- ject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, rst, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the eld. 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.

Seller Inventory # 9780387314099

Bibliographic Details

• Title: Series Approximation Methods in Statistics
• Publisher: Springer New York Apr 2006
• Publication Date: 2006
• Language: English
• ISBN 10: 0387314091
• ISBN 13: 9780387314099
• Binding: Taschenbuch
• Edition: 3rd Edition
• Condition: Neu
• Dimensions: 233W x 159H x 17D millimeters 233 millimeters width by 159 millimeters height by 17 millimeters depth
• Weight: 336 grams

About this title

Synopsis

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 s- ject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, ?rst, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the ?eld. 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.

About the Author

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