Distribution-Free Sufficiency in Sampling Finite Populations

Abstract

The concept of distribution-free sufficiency, (DF-sufficiency for short) for estimation in survey sampling, which has been introduced by Godambe (1966), is investigated. Uncorrelatedness in Godambe's definition is shown to be equivalent to statistical independence, as is claimed on the author's behalf in the appendix to Godambe's paper. But the second result claimed there, that every DF-sufficient estimate must necessarily be of the form