Kolassa J.E. Series Approximation Methods in Statistics

3rd ed. — Springer, 2006. — 228 p. — (Lecture Notes in Statistics, Vol. 88). — ISBN: 0387314091, 9780387314099.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 subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field.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.