In our study of UMVU estimation, we discovered that, for some models, if we restrict attention to the class of unbiased estimators there may be a best choice. Equivariant estimation is similar, but now we restrict attention to estimators that satisfy symmetry restrictions. At an abstract level, these restrictions are imposed using group theory. The basic ideas are developed here only for estimation of a location parameter, but we try to proceed in a fashion that illustrates the role of group theory.
KeywordsLoss Function Lebesgue Measure Location Parameter Risk Function Invariant Function
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