The Admissibility of a Preliminary Test Estimator When the Loss Incorporates a Complexity Cost
- 1 December 1979
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 74 (368) , 872
- https://doi.org/10.2307/2286414
Abstract
Consider the problem of estimating the mean by using a random sample from a normal population. Let denote the sample mean and consider the estimator that assumes the value zero when and the value when . 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.Keywords
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