FarmTest: Factor-Adjusted Robust Multiple Testing With Approximate False Discovery Control

Large-scale multiple testing with correlated and heavy-tailed data arises in a wide range of research areas from genomics, medical imaging to finance. Conventional methods for estimating the false discovery proportion (FDP) often ignore the effect of heavy-tailedness and the dependence structure amo...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of the American Statistical Association 2019-10, Vol.114 (528), p.1880-1893
Main Authors:	Fan, Jianqing, Ke, Yuan, Sun, Qiang, Zhou, Wen-Xin
Format:	Article
Language:	eng
Subjects:	Covariance Deviation Discovery Factor adjustment False discovery proportion Finance Huber loss Inequality Large-scale multiple testing Medical imaging Medical research Normality Power Robustness Robustness (mathematics) Statistical tests
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	Large-scale multiple testing with correlated and heavy-tailed data arises in a wide range of research areas from genomics, medical imaging to finance. Conventional methods for estimating the false discovery proportion (FDP) often ignore the effect of heavy-tailedness and the dependence structure among test statistics, and thus may lead to inefficient or even inconsistent estimation. Also, the commonly imposed joint normality assumption is arguably too stringent for many applications. To address these challenges, in this article we propose a factor-adjusted robust multiple testing (FarmTest) procedure for large-scale simultaneous inference with control of the FDP. We demonstrate that robust factor adjustments are extremely important in both controlling the FDP and improving the power. We identify general conditions under which the proposed method produces consistent estimate of the FDP. As a byproduct that is of independent interest, we establish an exponential-type deviation inequality for a robust U-type covariance estimator under the spectral norm. Extensive numerical experiments demonstrate the advantage of the proposed method over several state-of-the-art methods especially when the data are generated from heavy-tailed distributions. The proposed procedures are implemented in the R-package FarmTest. Supplementary materials for this article are available online.
ISSN:	0162-1459 1537-274X