Abstract #300170

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JSM 2003 Abstract #300170
Activity Number: 447
Type: Contributed
Date/Time: Thursday, August 7, 2003 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #300170
Title: A Note on Uniformly Most Powerful Invariant Tests in a One-Parameter Situation
Author(s): Nitis Mukhopadhyay*+
Companies: University of Connecticut
Address: Dept. of Statistics, Box U-4120, Storrs, CT, 06269-0001,
Keywords: maximal invariant ; UMPI test ; weight function ; Minimax approach ; Bayesian approach
Abstract:

We were not aware of explicit but non-trivial one-parameter hypotheses testing scenarios where only trivial uniformly most powerful invariant (UMPI) tests existed. We start with an interesting concrete example of a one-parameter hypotheses testing problem for which the associated maximal invariant does not lead to a practical solution. In this hypotheses testing problem, we briefly suggest two approaches to decide between the null and the alternative hypotheses. The first approach is frequentist in nature. It utilizes a weight function on the parameter space and compares "average" distributions under the null and the alternative hypotheses. The second approach is Bayesian in flavor. The note ends with other specific examples of reasonable hypotheses testing scenarios for which no non-trivial UMPI test exists.

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