Conditions governing the efficiency of adaptation algorithms which are based on the empirical Bayes approach to statistics

Abstract

Two empirical (based on the empirical Bayes approach) adaptation algorithms are considered for informational (i.e., with incomplete observation) non-Bayes systems. Their corresponding convergence rates are calculated, which are compared with the convergence rate of the optimal algorithm based on estimation of the maximum likelihood. The conditions for coincidence of the indicated rates whose fulfillment causes the considered empirical algorithms to be optimal are established. For one of the considered algorithms fulfillment of the optimality condition turns out to be possible when (and only when) the probability distribution of the observed random quantity allows the existence of efficient estimates of the unknown parameters.