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On the Structure of UMVUEs

Abstract

In all setups when the structure of UMVUEs is known, there exists a subalgebra \(\mathcal {U}\) (MVE-algebra) of the basic s-algebra such that all \(\mathcal {U}\)-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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Correspondence to Yaakov Malinovsky.

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Kagan, A.M., Malinovsky, Y. On the Structure of UMVUEs. Sankhya A 78, 124–132 (2016). https://doi.org/10.1007/s13171-015-0076-5

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  • DOI: https://doi.org/10.1007/s13171-015-0076-5

Keywords

  • Categorical data
  • Completeness
  • MVE-algebra
  • Sufficiency

AMS (2000) subject classification

  • Primary 62B99; Secondary 62F10
  • 62G05