Robust estimation using the Robbins-Monro stochastic approximation algorithm

The problem of minmax estimation of a location parameter introduced by Huber is considered. It is shown that under general conditions there exists a solution which is a form of the Robbins-Monro stochastic approximation algorithm. This generalizes earlier work by Martin and Masreliez who have given stochastic approximation (SA)-estimate solutions for two particular cases. As with the -estimate solutions given by Huber, the SA solutions are completely determined by the probability distribution function with least Fisher information in the distribution set used to model the observation errors.