Electronic Journal of Statistics

Identifiability of the proportion of null hypotheses in skew-mixture models for the p-value distribution

Subhashis Ghosal and Anindya Roy

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 329-341.

Dates
First available in Project Euclid: 10 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1305034905

Digital Object Identifier
doi:10.1214/11-EJS609

Mathematical Reviews number (MathSciNet)
MR2802046

Zentralblatt MATH identifier
1274.62109

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62G99: None of the above, but in this section

Keywords
Identifiability mixture models multiple testing skew-normal distribution

Citation

Ghosal, Subhashis; Roy, Anindya. Identifiability of the proportion of null hypotheses in skew-mixture models for the p-value distribution. Electron. J. Statist. 5 (2011), 329--341. doi:10.1214/11-EJS609. https://projecteuclid.org/euclid.ejs/1305034905


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