On Sequential Point Estimation in a Uniform Distribution with Adjusted Non-Sufficient Estimators : A Comparative Study and Real Data Illustration

Abstract

Abtsrcat The purely sequential minimum risk point estimation procedure for the unknown parameter θ (> 0) in a Uniform (0; θ) population has been discussed in this article. This is 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 are proposed. The unbiased estimators are randomly stopped versions of Χ n: n and X¯ n in either loss function. Performances of such estimators are compared. Clearly, using a randomly stopped version of X¯ n would amount to some loss of in- formation 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 ex- isting sequential estimators and illustrate our methodologies with the help of a real dataset.