Work

A generalized Fourier approach to estimating the null parameters and proportion of non-null effects in large-scale multiple testing

Year: 2009

Type: article

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.

Source: PubMed

DOI: 10.48550/arxiv.0911.3684

Authors: Jin, Jiashun, Peng, Jie, Wang, Pei

Institutions: Carnegie Mellon University, University of California, Davis, Fred Hutch Cancer Center

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Institute of General Medical Sciences

Awards: Statistical Analysis for Models involving Riemannian Manifolds, CAREER: Inferences on Large-Scale Multiple Comparisons: The Temptation of the Fourier Kingdom, Statistical Methods for Integrative Analysis of Genomics and Proteomics Data