An Approach to Deriving Equivariant Estimators

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.