Minimax robust estimation of location and minimizing fisher information

TLDR: In this article, the authors considered the minimax robust estimation of a location parameter as introduced by P. J. Huber, and proposed a Lagrange multiplier technique for calculating the probability distribution with minimum Fisher information over the associated distribution set.

Abstract: Asymptotic minimax robust estimation of a location parameter as introduced by P. J. Huber is considered. This problem is closely related to recent developments in robust detection theory and robust recursive filtering for linear systems. For a given minimax location estimation problem two distinct estimates which are solutions are determined by the probability distribution Fo which has minimum Fisher information over the associated distribution set. A Lagrange multiplier technique is given for calculating Fo for a broad class of distribution sets. Existence and uniqueness conditions for Fo are given.