Best linear equivariant estimation and prediction in location-scale families

In this paper, we derive representations of the best (affine) linear equivariant estimators (BLEEs) of the location and scale parameters in the location, scale, and location-scale set-ups. Furthermore, we show that the best linear equivariant predictor (BLEP) with respect to standardized mean squared error has a representation similar to the well known best linear unbiased predictor (BLUP). By analogy with the BLUP which depends on the best …