Purely Sequential Point Estimation of a Function of the Mean in an Exponential Distribution

Abstract

A purely sequential minimum risk point estimation methodology with an associated stopping time N is designed to come up with a unified strategy in an exponential distribution (Expo). We work under a weighted squared error loss due to the estimator $$g(\overline{X}_{N})$$ of $$g(\beta ),$$ a function of the unknown mean parameter $$\beta (>0)$$ , plus linear cost of sampling from an Expo $$(\beta )$$ population. A series of important first-order and second-order asymptotic (as c, the cost per unit sample, $$\rightarrow 0$$ ) results are laid out including (1) the first- and second-order efficiency properties, (2) the risk efficiency property, and (3) the second-order regret expansion under suitable conditions on g(.).