The best unbiased estimators in the absence of sufficiency and completeness

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Shams Mahdi; Hesamian Gholamreza

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Journal Paper

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Journal: MATHEMATICAL RESEARCHES Year:2023 | Volume:9 | Issue:3 Page(s): 35-55

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Information Journal Paper

Title

The best unbiased estimators in the absence of sufficiency and completeness

Author(s)

Shams Mahdi | Hesamian Gholamreza | Issue Writer Certificate

Keywords

Complete sufficient statistics

minimal sufficient statistics

uniformly minimum variance unbiased estimator

Fisher information

binary operation.

Abstract

In this study, a simple generalization of the Lehmann-Scheffe theorem is proposed in cases where UMVUEs exist but a sufficiently complete statistics does not exist. Also, another method is introduced based on the group action. In this method, UMVUE for the unknown parameter is found using a commutative and associative binary operation. Finally, the motivation for using the words "completeness" and "unbiasedness" is expressed in such a way that completeness and unbiasedness are not characteristic of a statistic or its parametric form, but a family of distributions of a statistic, and deleting even one point of the parameter space may change the completeness.

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