title: A GENERALIZED FOURIER APPROACH TO ESTIMATING THE NULL PARAMETERS AND PROPORTION OF NONNULL EFFECTS IN LARGE-SCALE MULTIPLE TESTING.
abstract: In a recent paper [4], Efron pointed out that an important issue in large-scale multiple hypothesis testing is that the null distribution may be unknown and need to be estimated. Consider a Gaussian mixture model, where the null distribution is known to be normal but both null parameters-the mean and the variance-are unknown. We address the problem with a method based on Fourier transformation. The Fourier approach was first studied by Jin and Cai [9], which focuses on the scenario where any non-null effect has either the same or a larger variance than that of the null effects. In this paper, we review the main ideas in [9], and propose a generalized Fourier approach to tackle the problem under another scenario: any non-null effect has a larger mean than that of the null effects, but no constraint is imposed on the variance. This approach and that in [9] complement with each other: each approach is successful in a wide class of situations where the other fails. Also, we extend the Fourier approach to estimate the proportion of non-null effects. The proposed procedures perform well both in theory and on simulated data.
authors.affiliation: Statistics Department, Carnegie Mellon University, Pittsburgh, PA.
authors.forename: Jiashun
authors.initials: J
authors.lastname: Jin
authors.affiliation: Statistics Department, University of California at Davis, Davis, CA.
authors.forename: Jie
authors.initials: J
authors.lastname: Peng
authors.affiliation: Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, Seattle, WA.
authors.forename: Pei
authors.initials: P
authors.lastname: Wang
keywords: Fourier transformation; empirical null; generalized Fourier transformation; proportion of non-null effects; sample size calculation