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August 2014 Single-index modulated multiple testing
Lilun Du, Chunming Zhang
Ann. Statist. 42(4): 1262-1311 (August 2014). DOI: 10.1214/14-AOS1222

Abstract

In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In this paper, we present a single-index modulated (SIM) multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate $p$-value, $(p_{1},p_{2})$, for each hypothesis, where $p_{1}$ is a preliminary $p$-value from prior information and $p_{2}$ is the primary $p$-value for the ultimate analysis. To find the optimal rejection region for the bivariate $p$-value, we propose a criteria based on the ratio of probability density functions of $(p_{1},p_{2})$ under the true null and nonnull. This criteria in the bivariate normal setting further motivates us to project the bivariate $p$-value to a single-index, $p(\theta)$, for a wide range of directions $\theta$. The true null distribution of $p(\theta)$ is estimated via parametric and nonparametric approaches, leading to two procedures for estimating and controlling the false discovery rate. To derive the optimal projection direction $\theta$, we propose a new approach based on power comparison, which is further shown to be consistent under some mild conditions. Simulation evaluations indicate that the SIM multiple testing procedure improves the detection power significantly while controlling the false discovery rate. Analysis of a real dataset will be illustrated.

Citation

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Lilun Du. Chunming Zhang. "Single-index modulated multiple testing." Ann. Statist. 42 (4) 1262 - 1311, August 2014. https://doi.org/10.1214/14-AOS1222

Information

Published: August 2014
First available in Project Euclid: 25 June 2014

zbMATH: 1297.62217
MathSciNet: MR3226157
Digital Object Identifier: 10.1214/14-AOS1222

Subjects:
Primary: 62P10
Secondary: 62G10 , 62H15

Keywords: $p$-value , Bivariate normality , local false discovery rate , multiple comparison , simultaneous inference , symmetry property

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 4 • August 2014
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