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The fixed sample size procedure sometimes fail to deal with the estimation problem in which it is desired to control the combined risk associated with the estimation of parameters of various probability distributions simultaneously. In this paper for a general probabilistic model is proposed an “accelerated” sequential class to minimize the combined risk for simultaneous estimation of parameters of several probability distributions. The proposed class is shown to provide solutions for many estimation problems under different probabilistic setups for “ given precision ” problems. Besides, positive and negative moments for the stopping times are obtained and they are used for deriving the asymptotic expression for the “regret” associated with the class of “accelerated” sequential estimation procedure.

An Accelerated Sequential Class to Minimize Combined Risk for Simultaneous Estimation of Parameters of Several