A Special Group Structure and Equivariant Estimation

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.