ASYMPTOTIC EXPANSIONS OF THE FISHER INFORMATION IN A SAMPLE-MEAN

Abstract

An asymptotic expansion for the information in an Edgeworth expandable random variable is obtained in terms of the cumulants and their derivatives. The obtained formula may be interpreted as an expansion about the exponential family. A noteworthy feature is that half integer powers in the sample size vanish. Applications to conditional inference and high order ancillarity are given, this being the main motivation of the study. © 1991.