On Optimal Estimation Methods Using Stochastic Approximation Procedures

Abstract

The problem of estimating the zero of a regression function by means of Robbins Monro type of stochastic approximation procedures is discussed. Optimality of the procedures is defined in terms of asymptotic variance. The discussion is restricted to the case of identically distributed errors. In that case we suggest transforming the observed random variables in order to minimize the asymptotic variance of the estimators. The optimal transformation turns out to depend on the underlying distribution of the errors and on the slope of the regression function at the zero.