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Series Approximation Methods in Statistics
This is approved bcc: 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. This second edition features an expanded list of references, exercises, and applications, a reordering of material facilitating a quick introduction to series expansions without thorough consideration of all of the theoretical results and regularity conditions, and an addition of material on efficiency and power calculations. John E. Kolassa is Assistant Professor of Biostatistics at the University of Rochester.
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.
Lecture notes in statistics (Springer-Verlag) ; 88