A note on universal admissibility of scale parameter estimators

The notion of universal admissibility of estimators was introduced and developed by Hwang (1985) and Brown and Hwang (1989). In several models commonly used estimators of scale parameters are shown to be inadmissible under specified loss functions. Here we focus on the scale and location-scale invariant estimation of the scale parameter under the universal admissibility criterion. For a one parameter gamma distribution, we characterize the class of universal admissible estimators. For the two parameter normal and exponential models we derive the condition for universal inadmissibility of the estimators of the scale parameter.