Asymptotically Efficient Stochastic Approximation; The RM Case

Abstract

Anbar (1971) and, independently, Abdelhamid (1971) have shown that if the density $g$ of the errors of estimates of function values is known, a transformation of observations leads to stochastic approximation methods which under mild conditions produce asymptotically efficient estimators (the first author considers the RM case, the second the RM and KW cases). This paper treats the RM case and shows that the same asymptotic result can be achieved without the knowledge of the density $g$.