Simultaneous Equivariant Estimation for Location - Scale Models with a Common Scale Parameter

Abstract

In this paper, we develop a procedure for simultaneous equivariant estimation of the pa rameters of location - scale models having a common scale parameter. Minimum risk equivariant (MRE) estimator is determined for any invariant loss function. MRE estimator is characterized with respect to a quadratic- type loss function (Zacks, 1971, p. 102) and its uniqueness is observed . Four optimality criteria for comparing vector equivariant estimators are considered and their equivalence is established .