On the structure of UMVUEs

In all setups when the structure of UMVUEs is known, there exists a subalgebra $\cal U$ (MVE-algebra) of the basic $σ$-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.

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