Series Approximation Methods in Statistics - Lecture Notes in Statistics S.

This study covers the uses of series approximation techniques in statistics and is intended to give advanced graduate students in statistics an introduction to various expansions. Its aims are to provide a rigorous development of these expansions, with attention paid to regularity conditions and uniformity, and to survey applications of these series.;Topics include characteristic functions and the Berry-Esseen Theorem, Edgeworth series, saddlepoint series for densities and distribution functions, multivariate expansions, conditional distribution approximations, and applications to likelihood ratio and maximum likelihood statistics.;The use of a computerized algebra program for performing many of the calculations in this volume is demonstrated.;The author presupposes a knowledge of undergraduate real and complex analysis, but otherwise the book is essentially self-contained. It is based on lecture courses given by the author, and will also be of use to researchers seeking a sophisticated account of an area of recent research activity.