Open Access
2011 Identifiability of the proportion of null hypotheses in skew-mixture models for the p-value distribution
Subhashis Ghosal, Anindya Roy
Electron. J. Statist. 5: 329-341 (2011). DOI: 10.1214/11-EJS609


In many multiple testing procedures, accurate modeling of the p-value distribution is a key issue. Mixture distributions have been shown to provide adequate models for p-value densities under the null and the alternative hypotheses. An important parameter of the mixture model that needs to be estimated is the proportion of true null hypotheses, which under the mixture formulation becomes the probability mass attached to the value associated with the null hypothesis. It is well known that in a general mixture model, especially when a scale parameter is present, the mixing distribution need not be identifiable. Nevertheless, under our setting for mixture model for p-values, we show that the weight attached to the null hypothesis is identifiable under two very different types of conditions. We consider several examples including univariate and multivariate mixture models for transformed p-values. Finally, we formulate an abstract theorem for general mixtures and present other examples.


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Subhashis Ghosal. Anindya Roy. "Identifiability of the proportion of null hypotheses in skew-mixture models for the p-value distribution." Electron. J. Statist. 5 329 - 341, 2011.


Published: 2011
First available in Project Euclid: 10 May 2011

zbMATH: 1274.62109
MathSciNet: MR2802046
Digital Object Identifier: 10.1214/11-EJS609

Primary: 62E10
Secondary: 62G99

Keywords: Identifiability , Mixture models , multiple testing , skew-normal distribution

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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