Series Approximation Methods in Statistics

ISBN-13: 9780387314099 / Angielski / Miękka / 2006 / 222 str.

John E. Kolassa; John Edward Kolassa

Opis

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.

Recenzje

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)

Spis treści

Asymptotics in General.- Characteristic Functions and the Berry-Esseen Theorem.- Edgeworth Series.- Saddlepoint Series for Densities.- Saddlepoint Series for Distribution Functions.- Multivariate Expansions.- Conditional Distribution Approximations.- Applications to Wald, Likelihood Ratio, and Maximum Likelihood Statistics.- Other Topics.- Computational Aids.

O autorze

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