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arXiv · 1507.02769

On the structure of UMVUEs

Abram M. Kagan·Yaakov Malinovsky
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Abstract

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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Abram M. Kagan, Yaakov Malinovsky. 2015-07-10. On the structure of UMVUEs. https://doi.org/10.1007/s13171-015-0076-5

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