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We consider the problem of minimum risk point estimation of the mean of an exponential distribution under the assumption that the mean exceeds some positive known number. For this problem Mukhopadhyay and Duggan (2001) proposed a two-stage procedure and provided second-order approximations to the lower and upper bounds for the regret. Under the same set up we give second-order approximations to the regret and compare our approximations with those of them. It turns out that our bounds for the regret are sharper. We also propose a bias-corrected procedure which reduces the risk. <br /

On Second-order Approximations to the Risk in Estimating the Exponential Mean by a Two-stage Procedure