A NOTE ON ACCELERATED SEQUENTIAL ESTIMATION OF THE MEAN OF NEF-PVF DISTRIBUTIONS

ARUP BOSE^{1} AND NITIS MUKHOPADHYAY^{2}

1Stat-Math Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Calcutta 700 035, India 2Department of Statistics, University of Connecticut, UBox 120, 196 Auditorium Road, Storrs, CT 06269, U.S.A.

(Received December 20, 1993)

Abstract. The minimum risk point estimation for the mean is addressed for a natural exponential family (NEF) that also has a power variance function (PVF) under a loss function given by the squared error plus linear cost. An appropriate accelerated version of the full purely sequential methodology of Bose and Boukai (1993b, submitted) is proposed along the lines of Mukhopadhyay (1993a, Tech. Report, No. 93-27, Department of Statistics, University of Connecticut) in order to achieve operational savings. The main result provides the asymptotic second-order expansion of the regret function associated with the accelerated sequential estimator of the population mean.

Key words and phrases: Natural exponential family, power variance function, mean estimation, minimum risk, acceleration, regret expansion, operational savings.