Asymptotically Efficient Estimation of Location for a Symmetric Stable Law

Abstract

A well-known characteristic function representation of the family of symmetric stable distributions $\mathscr{F}$ indexes them with a location, scale, and type parameter. A sample of size $n$ is taken from an unknown member of $\mathscr{F}$. In this paper, an estimator of the location parameter is constructed which is maximum probability. This means that the estimator conventionally normalized converges in distribution to a normal distribution with zero mean and variance the inverse of the Fisher Information.