Non-Sufficiency Via Conditioning Arguments with Illustrations

Abstract

Abtsrcat We reiterate a conditioning approach to highlight that | X| may not be a sufficient statistic for θ when original data X follows certain specific well-known distributions. The approach requires one to show that the conditional distribution of X given | X| involves θ Our examples and commentaries are expected to lead to more appreciation of the notion of sufficiency (or non-sufficiency).