On the Choice of Starting Point in Stochastic Approximation

Abstract

Consider the problem of point estimation of a location parameter θ of a symmetric distribution by way of a Robbins-Monro stochastic approximation recursive approach, particularly the choice of starting random variable. Conditions on the starting variable are given to guarantee that at each step the estimator is unbiased and translation invariant. Finally, a Monte Carlo study is done to compare the behavior of the procedures started by some random variables when the sample size is small and the underlying distribution is long tailed.