On weakly equivariant estimators

In this paper, we shall generalize the concept of equivariance in statistics to “weak equivariance”. Then, we summarize the properties of weakly equivariant estimators and their applications in statistics. At first we characterize the class of all weakly equivariant estimators. Then, we shall consid...

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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Germany), 2021-08, Vol.62 (4), p.1611-1650
Main Author: Shams, M.
Format: Article
Language:English
Subjects:
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Estimators
Finance
Insurance
Management
Mathematics and Statistics
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Regular Article
Risk
Statistics
Statistics for Business
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Summary:In this paper, we shall generalize the concept of equivariance in statistics to “weak equivariance”. Then, we summarize the properties of weakly equivariant estimators and their applications in statistics. At first we characterize the class of all weakly equivariant estimators. Then, we shall consider the concept of cocycles and isovariance, and so we find their connection with weakly equivariant functions. It is natural to restrict attention to the class of weakly equivariant estimator to find minimum risk weakly equivariant estimators. If the group acts in two different ways, we shall find a relation between the minimum risk equivariant and minimum risk weakly equivariant estimator under the old and new group actions. Also we shall introduce a necessary and sufficient condition for the invariance of the loss function under the new action.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-019-01149-0