Volume 9, Issue 3 (12-2023)
mmr 2023, 9(3): 35-55 |
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Shams M, Hesamian G. The best unbiased estimators in the absence of sufficiency and completeness. mmr 2023; 9 (3) :35-55
URL: http://mmr.khu.ac.ir/article-1-3221-en.html
URL: http://mmr.khu.ac.ir/article-1-3221-en.html
1- University of Kashan , mehdi_shams1357@yahoo.com
2- Payame Noor University
2- Payame Noor University
Abstract: (607 Views)
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.
Keywords: Complete sufficient statistics, minimal sufficient statistics, uniformly minimum variance unbiased estimator, Fisher information, binary operation.
Type of Study: Original Manuscript |
Subject:
stat
Received: 2021/08/15 | Revised: 2024/02/19 | Accepted: 2022/02/21 | Published: 2024/02/6 | ePublished: 2024/02/6
Received: 2021/08/15 | Revised: 2024/02/19 | Accepted: 2022/02/21 | Published: 2024/02/6 | ePublished: 2024/02/6
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