Minimum Convex Risk Equivariant Finite Population Prediction for Linear Functions in Regression Models

Abstract

This paper addresses the problem of equivariant prediction of linear functions in a finite population under a linear regression superpopulation model. Of particular interest is the finite population total. A theorem that gives a necessary and sufficient condition for a predictor to be minimum risk equivariant predictor of any linear function with respect to a convex loss function is established. Illustrative examples are discussed.