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A special group structure common to many statistical problems is presented. In the context of equivariant estimation, this leads to a characterization of equivariant estimators (Section 3). Under further conditions, measurable equivariant estimators are characterized (Section 4). Some examples are presented in Section 5 and Section 6 contains a brief discussion of related work in which the special group structure is useful.
Robert H. Berk (Sun,) studied this question.