Sequential estimation via replicated piecewise stopping number in a tow—parameter exponential family of distributions

Abstract

In a certain class of two—parameter exponential distributions, we consider minimum risk point estimation problems for one of the parameters. We propose to implement the sequential procedure of Bose and Boukai (1993) in smaller “pieces” along the lines of Mukhopadhyay and Sen (1993). Unlike the fully sequential procedure, one can obtain an unbiased estimator for the variance of the storpping number in a piecewise methodology. On top of this, the asymptotic second—order expansions of the regret functions for both the piecewise and fully sequential estimators are same up to o(1) term and the piecewise sampling scheme is operationally more covenient. The effect on cost due to parallel processing is also discussed