An Approach to Deriving Equivariant Estimators
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Mehdi Shams * , Mehdi Emadi , Naser Reza Arghami |
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Abstract: (14923 Views) |
In this paper the class of all equivariant is characterized functions. Then two conditions for the proof of the existence of equivariant estimators are introduced. Next the Lehmann's method is generalized for characterization of the class of equivariant location and scale function in terms of a given equivariant function and invariant function to an arbitrary group family. This generalized method has applications in mathematics, but to make it useful in statistics, it is combined with a suitable function to make an equivariant estimator. This of course is usable only for unique transitive groups, but fortunately most statistical examples are of this sort. For other group equivariant estimators are directly obtained. |
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Keywords: Topological group, Group action, Homogeneous space, Sharply transitivity, Invariance, Equivariance, Isovariance. |
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Full-Text [PDF 442 kb]
(2846 Downloads)
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Type of Study: Research |
Subject:
Statistical Inference Received: 2012/09/8 | Accepted: 2013/05/14 | Published: 2013/05/14
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