Robustized vector Robbins-Monro algorithm with applications to m-interval detection

In this paper a convergence theorem for the vector version of the Robbins-Monro procedure with adaptive gain matrices is established. This theorem is then applied to obtain a recursive estimator of the quartiles of a distribution using adaptive gain matrices and batch processing of the samples. In addition, a recursive method of density function estimation provides another short illustration of the applicability of this method to information processing problems. Although only two practical applications are given in this paper, the theorem has much broader implications as a generalized robustized vector recursive algorithm.