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On Recovering Lost Information for Sequential Estimation in a Uniform Distribution

The purely sequential minimum risk point estimation procedure for the unknown parameter θ (> 0) in a U(0, θ) population has been discussed in this article. This was developed under a squared error loss plus a linear cost function of sampling. The unknown parameter θ is estimated by means of four different estimators in the stopping rule, where as in the loss function two different unbiased estimators of θ were proposed. However, the unbiased estimators are randomly stopped versions of Xn:n and 2Xn in either loss function. Performances of such estimators are compared. Clearly, using a randomly stopped version of 2Xn would amount to some loss of information when compared with a corresponding randomly stopped largest sample order statistic under both loss functions and the stopping rules. In this paper, we explore a novel approach to recover any loss of information by fine-tuning the loss function and then properly tailoring the associated sequential methodologies. We examine how the sequential risks of our newly proposed methodologies would compare with those associated with the existing sequential estimators. Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Session STS005) p.2058