(Received June 19, 1992; revised November 9, 1992)
Abstract. We consider the problem of minimum risk point estimation for the parameter theta = amu+bsigma of the exponential distribution with unknown location parameter mu and scale parameter sigma when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of theta and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989, South African Statist. J., 23, 251-268).
Key words and phrases: Two-parameter exponential, asymptotically unbiased estimator, sequential estimator, uniform integrability, second order.