Title: On the Structure of UMVUEs

Author(s): Abram M. Kagan and Yaakov Malinovsky
Issue: Volume 78 Series A Part 1 Year 2016
Pages: 124 -- 132
In all setups when the structure of UMVUEs is known, there exists a sub-algebra ${\cal U}$ (MVE-algebra) of the basic $\sigma$-algebra such that all ${\cal U}$-measurable statistics with finite second moments are UMVUEs. It is shown that MVE-algebras are, in a sense, similar to the subalgebras generated by complete sufficient statistics. Examples are given when these subalgebras differ, in these cases a new statistical structure arises.
AMS (2000) subject classification. Primary 62B99; Secondary 62F10, 62G05.
Keywords and phrases: Categorical data, Completeness, MVE-algebra, Sufficiency.