Relation of the Best Invariant Predictor and the Best Unbiased Predictor in Location and Scale Families

Abstract

In this paper a necessary and sufficient condition for a predictor to be the best invariant predictor in location and scale families is given. Using this condition, it is shown that the best invariant predictor is expressed by a linear combination of the best unbiased predictor and the best unbiased estimator of the scale parameter.