SEQUENTIAL ESTIMATION OF A PARAMETER OF AN EXPONENTIAL DISTRIBUTION

EIICHI ISOGAI AND CHIKARA UNO

Department of Mathematics, Niigata University, 8050 Ikarashi 2-cho, Niigata 950-21, Japan

(Received June 19, 1992; revised November 9, 1992)

Abstract. We consider the problem of minimum risk point estimation for the parameter θ = aμ + bσ of the exponential distribution with unknown location parameter μ and scale parameter σ when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of θ 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.