A Note on Hyperadmissibility of Estimators for Finite Populations

Abstract

A condition on the sampling design which previously [2] was shown to be a sufficient condition for the Horvitz-Thompson estimator to be the unique hyperadmissible estimator of the population total is now shown to be a necessary condition also save for trivial exceptions. The exceptions are the sampling designs in which the only samples with positive probability are such that they include the whole population.