ESTIMATION OF THE MEAN VECTOR OF A MULTIVARIATE NORMAL MODEL UNDER REFLECTED NORMAL LOSS

Abstract

For estimating an unknown mean vector-parameter in a multivariate normal
population, we propose the unrestricted, restricted and preliminary test estima-
tors 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.