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Cover Art
Author Kolassa, John Edward, 1963-

Title Series approximation methods in statistics / John E. Kolassa.

Published New York : Springer, [1997]


Location Call No. Status
 UniM ERC  519.532 KOLA    AVAILABLE
Edition 2nd ed.
Physical description xi, 183 pages : illustrations ; 24 cm.
Series Lecture notes in statistics ; 88.
Lecture notes in statistics (Springer-Verlag) ; v. 88.
Bibliography Includes bibliographical references (pages 172-179) and indexes.
Contents 1. Asymptotics in General -- 2. Characteristic Functions and the Berry-Esseen Theorem -- 3. Edgeworth Series -- 4. Saddlepoint Series for Densities -- 5. Saddlepoint Series for Distribution Functions -- 6. Multivariate Expansions -- 7. Conditional Distribution Approximations -- 8. Applications to Wald, Likelihood Ratio, and Maximum Likelihood Statistics -- 9. Other Topics -- 10. Computational Aids.
Summary This 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. This book is intended primarily for advanced graduate students and researchers in the field needing a collection of core results in a uniform notation, with bibliographical references to further examples and applications. It assumes familiarity with real analysis, vector calculus, and complex analysis.
Subject Mathematical statistics -- Asymptotic theory.
Asymptotic distribution (Probability theory)
Edgeworth expansions.
ISBN 0387982248 (paperback: alk. paper)