Abstract
The problem of Bayes sequential estimation of the unknown parameter in a particular exponential family of distributions is considered under linear exponential loss function for estimation error and a fixed cost for each observation. Instead of fully sequential sampling, a two-stage sampling technique is introduced to solve the problem in this paper. The proposed two-stage procedure is robust in the sense that it does not depend on the parameters of the conjugate prior. It is shown that the two-stage procedure is asymptotically pointwise optimal and asymptotically optimal for a large class of the conjugate priors. A simulation study is conducted to compare the performances of the two-stage procedure and the purely sequential procedure.
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