Simultaneous estimation of location parameters of the distribution with finite support

Abstract

SummaryLet X~, i=l,...,p be the ith component of the px1 vector X= (X,, X~,..., X~,)'. Suppose that XL, X~,..-, X~ are independent and that X, has a probability density which is positive on a finite interval, is symmetric about G and has the same variance. In estimation of the location vector ~=(8~, 82,..., G)' under the squared error loss function explicit estimators which dominate X are obtained by using integration by parts to evaluate the risk function. Further, explicit dominating estimators are given when the distributions of X,'s are mixture of two uniform distributions. For the loss function L(d, o)=ll~-stl 4 such an estimator is also given when the distributions of X,'s are uniform distributions.