Optimality of Royall's predictor under a Gaussian superpopulation model

Abstract

This note shows that under the assumption of a Gaussian superpopulation model with a general symmetric and positive-definite covariance matrix, the model-based predictor of Royall (1976) is the unbiased minimum mean squared error predictor of the total of a given finite population. This somewhat anticipated result is a generalization of recent published work in which it was derived under more restrictive assumptions.