A note on multiple testing for composite null hypotheses |
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Authors: | Stefano Cabras |
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Affiliation: | Department of Mathematics, University of Cagliari, Via Ospedale 72, 09124 Cagliari, Italy |
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Abstract: | Multiple hypothesis testing literature has recently experienced a growing development with particular attention to the control of the false discovery rate (FDR) based on p-values. While these are not the only methods to deal with multiplicity, inference with small samples and large sets of hypotheses depends on the specific choice of the p-value used to control the FDR in the presence of nuisance parameters. In this paper we propose to use the partial posterior predictive p-value [Bayarri, M.J., Berger, J.O., 2000. p-values for composite null models. J. Amer. Statist. Assoc. 95, 1127–1142] that overcomes this difficulty. This choice is motivated by theoretical considerations and examples. Finally, an application to a controlled microarray experiment is presented. |
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Keywords: | Composite null hypothesis Elimination of nuisance parameters False discovery rate Partial posterior predictive p-values Positive false discovery rate |
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