Generalizations of Rao–Blackwell and Lehmann–Scheffé Theorems with Applications

Abstract

Our aim in this paper is extending the applicability domain of the Rao–Blackwell theorem, our methodology is using conditional expectation and generalizing sufficient statistics, and one result is a generalization of the Lehmann–Scheffé theorem; as a conclusion, some problems that could not be solved by an earlier version of the Lehmann–Scheffé theorem become solvable by our new generalization.

Keywords

• complete minimal sufficient statistic
• incomplete minimal sufficient statistic
• minimal sufficient statistic
• Rao–Blackwell theorem
• sufficient statistic