Multivariate Asymptotically Optimal Stochastic Approximation Procedure

The authors consider the problem of estimating the root of the regression equation in the multivariate case. It is shown that if there exists an estimate that converges to the unknown value of the root at some rate, then it can be used, practically without any additional conditions, to construct a recursive procedure of stochastic-approximation type which is optimal in the sense of the minimum covariance matrix of the limiting normal law.