An Application of a Theorem of Robbins and Siegmund

Abstract

A stochastic approximation process for estimating an unknown parameter in nonlinear regression is discussed. The process was suggested by Albert and Gardner [Stochastic Approximation and Nonlinear Regression. Research Monograph No. 42. M.I.T. Press, Cambridge, Massachusetts]. An almost sure convergence of the process is proved. The proof is an application of a theorem of Robbins and Siegmund on the almost sure convergence of nonnegative almost supermatingales. The conditions given here are weaker than those given by Albert and Gardner.