Equivariance

Abstract

In Chapter 3, we introduced a few principles of classical decision theory (e.g., minimaxity, ancillarity) to help to choose among admissible rules. In Chapter 5, we introduced another principle called unbiasedness which could be used to select a subset of the class of all estimators. As we saw, sometimes none of the unbiased estimators was admissible. In this chapter, we introduce another ad hoc principle called equivariance,¹ which can also be used to select a subset of the class of all estimators. The principle of equivariance, in its most general form, relies on the algebraic theory of groups. However, the basic concept can be understood by means of a simple class of problems in which the principle can apply.