On weakly equivariant estimators

  • M. ShamsEmail author
Regular Article


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.


Topological group Hausdorff space Locally compact group Orbit type Transitivity Homogeneous space Invariance Isovariance Weakly equivariance Cocycles 

Mathematics Subject Classification

Primary 62F10 Secondary 54H11 



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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of Mathematical SciencesUniversity of KashanKashanIran

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