ESTIMATION OF AN EXPONENTIAL QUANTILE UNDER A GENERAL LOSS AND AN ALTERNATIVE ESTIMATOR UNDER QUADRATIC LOSS

CONSTANTINOS PETROPOULOS AND STAVROS KOUROUKLIS

Department of Mathematics, University of Patras, 26 500 Rio, Patras, Greece, e-mail: stavros@math.upatras.gr

(Received November 22, 1999; revised April 5, 2000)

Abstract. Estimation of the quantile μ + κσ of an exponential distribution with parameters (μ, σ) is considered under an arbitrary strictly convex loss function. For κ obeying a certain condition, the inadmissibility of the best affine equivariant procedure is established by exhibiting a better estimator. The LINEX loss is studied in detail. For quadratic loss, sufficient conditions are given for a scale equivariant estimator to dominate the best affine equivariant one and, when κ exceeds a lower bound specified below, a new minimax estimator is identified.

Key words and phrases: Decision theory, Stein technique, Brewster and Zidek technique, equivariant estimation.