Series Approximation Methods In Statistics

This book presents theoretical results relevant to Edgeworth and saddlepointexpansions to densities and distribution functions. It provides examples oftheir app... » 

This book presents theoretical results relevant to Edgeworth and saddlepointexpansions to densities and distribution functions. It provides examples oftheir application in some simple and a few complicated settings along withnumerical as well as asymptotic assessments of their accuracy. Variants onthese expansions including much of modern likelihood theory are discussed andapplications to lattice distributions are extensively treated. This book isintended primarily for advanced graduate students and researchers in the fieldneeding a collection of core results in a uniform notation withbibliographical references to further examples and applications. It assumesfamiliarity with real analysis vector calculus and complex analysis. Thisthird edition features an expansion of the material on the Blackwellapproximation and an expansion of the discussions on saddlepoint approximation.TOCAsymptotics in General.. Characteristic Functions and the BerryEsseenTheorem. Edgeworth Series. Saddlepoint Series for Densities. SaddlepointSeries for Distribution Functions. Multivariate Expansions. ConditionalDistribution Approximations. Applications to Likelihood Ratio and MaximumLikelihood Statistics. Other Topics. Computational Aids. «