Approximations for Densities of Sufficient Estimators

Abstract

Durbin (1980a) proposed a simple method for obtaining asymptotic expansions for the densities of sufficient estimators. The expansion is a series which is effectively in powers of n-1, where n is the sample size, as compare with the Edgeworth expansion which is in powers of n-1/2. The basic approximation is just the first term of this series. This has an error of order n-1 compare to the error of n-1/2 in the usual asymptotic normal approximation. The order of magnitude of the error can generally be reduced to order n-3/2 by renormalization.