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Shams M. Independence of sufficient equivariant statistics and invariant statistics under topological groups. mmr 2026; 11 (4) :8-30
URL: http://mmr.khu.ac.ir/article-1-3432-en.html
URL: http://mmr.khu.ac.ir/article-1-3432-en.html
University of Kashan , mehdi_shams1357@yahoo.com
Abstract: (163 Views)
In statistics, the existence of independence between statistics is of particular importance.
Without calculating the joint distribution of two statistics, the existence of this independence is proven by meeting the necessary conditions,
including the sufficient completeness of one statistic and the ancillarity of the other.
In this paper, generalizations of this issue, as well as the cases of countably completeness and Bayesian framework , will be examined.
Finally, under the action of topological groups,
this fact is generalized and the independence of a sufficiently equivariant and invariant function is proven.
Without calculating the joint distribution of two statistics, the existence of this independence is proven by meeting the necessary conditions,
including the sufficient completeness of one statistic and the ancillarity of the other.
In this paper, generalizations of this issue, as well as the cases of countably completeness and Bayesian framework , will be examined.
Finally, under the action of topological groups,
this fact is generalized and the independence of a sufficiently equivariant and invariant function is proven.
Keywords: Group action, countably completeness, pairwise sufficiency, Bayesian perspective, invariance, equivariance.
Type of Study: Original Manuscript |
Subject:
stat
Received: 2024/11/22 | Revised: 2026/02/26 | Accepted: 2025/11/2 | Published: 2026/01/19 | ePublished: 2026/01/19
Received: 2024/11/22 | Revised: 2026/02/26 | Accepted: 2025/11/2 | Published: 2026/01/19 | ePublished: 2026/01/19
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