Series Approximation Methods in Statistics

John E. Kolassa (auth.)9780387322278, 0-387-32227-2, 9780387314099, 0387314091

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 and univariate complex analysis, and vector calculus.

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Table of contents :
Front Matter….Pages N2-viii
Asymptotics in General….Pages 1-4
Characteristic Functions and the Berry-Esseen Theorem….Pages 5-20
Edgeworth Series….Pages 21-48
Saddlepoint Series for Densities….Pages 49-69
Saddlepoint Series for Distribution Functions….Pages 70-80
Multivariate Expansions….Pages 81-94
Conditional Distribution Approximations….Pages 95-111
Applications to Likelihood Ratio and Maximum Likelihood Statistics….Pages 112-131
Other Topics….Pages 132-137
Computational Aids….Pages 138-142
Back Matter….Pages 143-153