AISM 53, 746-759
© 2001 ISM

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,

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

Abstract.    Estimation of the quantile $\mu + \kappa \sigma$ of an exponential distribution with parameters $(\mu , \sigma)$ is considered under an arbitrary strictly convex loss function. For $\kappa$ 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 $\kappa$ 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.

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