More on the inadmissibility of step-up |
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Authors: | Arthur Cohen |
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Institution: | Department of Statistics, Rutgers University, Piscataway NJ 08854-8019, USA |
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Abstract: | Cohen and Sackrowitz Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure, Ann. Statist. 33 (2005) 145-158] proved that the step-up multiple testing procedure is inadmissible for a multivariate normal model with unknown mean vector and known intraclass covariance matrix. The hypotheses tested are each mean is zero vs. each mean is positive. The risk function is a 2×1 vector where one component is average size and the other component is one minus average power. In this paper, we extend the inadmissibility result to several different models, to two-sided alternatives, and to other risk functions. The models include one-parameter exponential families, independent t-variables, independent χ2-variables, t-tests arising from the analysis of variance, and t-tests arising from testing treatments against a control. The additional risk functions are linear combinations where one component is the false discovery rate (FDR). |
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Keywords: | 62H15 62C15 |
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