Sufficient admissibility conditions for scale parameter estimator

Although there are a number of results available for the admissibility of the best translation equivariant estimator of the parameter, there is hardly any stated explicitly for the best scale equivariant estimator of the scale parameter. In this paper, we derive sufficient conditions for the admissibility of the scale parameter estimators and compara them. The derivations use the well known results due to Brown 1], Farrell 2], and Portnoy 3]. The loss function has been taken to be quadratic.