The admissibility of a preliminary test estimator when the loss incorporates a complexity cost

Consider the problem of estimating the mean by using a random sample from a normal population. Let (Equation presented) denote the sample mean and consider the estimator that assumes the value zero when (Equation presented) and the value (Equation presented) when (Equation presented). This is called a preliminary test estimator. For most of the usual loss functions it is inadmissible. In this article we show that for some loss functions, which include a complexity cost, the estimator is admissible. The results are related to Cohen’s work on hybrid estimation and hypothesis-testing problems. © 1979, Taylor & Francis Group, LLC.