## Article

#### Title: On the Structure of UMVUEs

##### Issue: Volume 78 Series A Part 1 Year 2016
###### Abstract
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.