On the structure of UMVUEs

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 \(\sigma\)-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 gene...

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Veröffentlicht in:arXiv.org 2015-07
Hauptverfasser: Kagan, Abram M, Malinovsky, Yaakov
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematics - Statistics Theory
Statistics - Theory
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Zusammenfassung:In all setups when the structure of UMVUEs is known, there exists a subalgebra \(\cal U\) (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.
ISSN:2331-8422
DOI:10.48550/arxiv.1507.02769