Series Approximation Methods in Statistics

Paperback | April 28, 2006

byJohn E. Kolassa

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This revised book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. It provides examples of their application in some simple and a few complicated settings, along with numerical, as well as asymptotic, assessments of their accuracy. Variants on these expansions, including much of modern likelihood theory, are discussed and applications to lattice distributions are extensively treated.

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This revised book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. It provides examples of their application in some simple and a few complicated settings, along with numerical, as well as asymptotic, assessments of their accuracy. Variants on these expansions, inclu...

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John E. Kolassa is Assistant Professor of Biostatistics at the University of Rochester.
Format:PaperbackDimensions:232 pages, 9.02 × 5.98 × 0.03 inPublished:April 28, 2006Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387314091

ISBN - 13:9780387314099

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Table of Contents

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 Likelihood Ratio and Maximum Likelihood Statistics.- Other Topics.- Computational Aids.

Editorial Reviews

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)