Volume 8, Issue 4 (Vol. 8,No. 4, 2022)
mmr 2022, 8(4): 94-119 |
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Shams M. An Approach to Deriving Maximal Invariant Statistics. mmr 2022; 8 (4) :94-119
URL: http://mmr.khu.ac.ir/article-1-3121-en.html
URL: http://mmr.khu.ac.ir/article-1-3121-en.html
University of Kashan , mehdi_shams1357@yahoo.com
Abstract: (568 Views)
Invariance principles is one of the ways to summarize sample information and by these principles invariance or equivariance decision rules are used. In this paper, first, the methods for finding the maximal invariant function are introduced. As a new method, maximal invariant statistics are constructed using equivariant functions. Then, using several equivariant functions, the maximal invariant statistic is obtained. If the group acts uniquely transitively, the equivariant functions will be converted into estimators that can be used in statistical branches. Finally, it is shown that in the case that the group action is not uniquely transitive but a normal subgroup has this property, the maximal invariant statistic can also be calculated.
Keywords: maximal invariant statistic, equivariant estimator, stability subgroup, normal subgroup.
Type of Study: Original Manuscript |
Subject:
stat
Received: 2020/08/4 | Revised: 2023/06/17 | Accepted: 2021/01/31 | Published: 2022/12/31 | ePublished: 2022/12/31
Received: 2020/08/4 | Revised: 2023/06/17 | Accepted: 2021/01/31 | Published: 2022/12/31 | ePublished: 2022/12/31
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