estimation of the mean vector of a multivariate normal model under reflected normal loss

Abstract

For estimating an unknown mean vector-parameter bt in a multivariate normal population, we propose the unrestricted, restricted and preliminary test estimators and derive their exact risk expressions under a modified reflected normal loss function. This approach is an extension to the work of Giles [2002. Preliminary-Test and Bayes Estimation of A Location Parameter Under Reflected Normal Loss, in Ullah, A. and Chaturvedi, A, Handbook of Applied Econometrics and Statistical Inference, Marcel Decker, New York, 287-303]. Comparison are then made for more clarity of the behavior of the estimators.