Simultaneous estimation of location parameters of the distribution with finite support

Summary

LetX _i ,i=1,..., p be theith component of thep×1 vectorX=(X₁,X₂,...,X _p )′. Suppose thatX₁,X₂,...,X _p are independent and thatX _i has a probability density which is positive on a finite interval, is symmetric about θ _i and has the same variance. In estimation of the location vector θ=(θ₁, θ₂,...,θ _p )′ under the squared error loss function explicit estimators which dominateX are obtained by using integration by parts to evaluate the risk function. Further, explicit dominating estimators are given when the distributions ofX _i ′s are mixture of two uniform distributions. For the loss function$L(\hat \theta ,\theta ) = ||\hat \theta - \theta ||^4$ such an estimator is also given when the distributions ofX _i ′s are uniform distributions.