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

Abstract

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 paper we propose a Factor-Adjusted Robust Multiple Testing (FarmTest) procedure for largescale simultaneous inference with control of the false discovery proportion. 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 exponentialtype 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.

A projection-based conditional dependence measure with applications to high-dimensional undirected graphical models

“…Liu (2013) proposed a procedure for estimating large Gaussian graphical models with FDR control. Fan et al (2018) proposed dependencyadjusted tests by estimating the latent factors that drive the dependency of these tests. In this work, we will follow the most commonly used Benjamini and Hochberg (BH) procedure developed in the seminal work of Benjamini & Hochberg (1995), where P-values of all marginal tests are compared.…”

Robust modifications of U-statistics and applications to covariance estimation problems

“…n can itself be viewed as an estimator of the covariance matrix. It has been proposed in [33] (see Remark 7 in that paper), and its performance has been later analyzed in [16] (see Theorem 3.2). These results support the claim that a small number of gradient descent steps for problem (3.3) suffice in applications.…”

“…The present paper can be seen as a direct extension of these ideas to the case of matrix-valued U-statistics, and continues the line of work initiated in [15] and [33]; the main advantage of the techniques proposed is that they result in estimators that can be computed efficiently, and cover scenarios beyond covariance estimation problem. Recent advances in this direction include the works [16] and [34] that present new results on robust covariance estimation; see Remark 4.1 for more details.…”

High-dimensional factor model and its applications to statistical machine learning

“…文献 [108,116] 考虑了近似因子模型下的 FDP 估计, 文献 [117] 研究了同时具有观测变量和潜因子的复杂模型, 文 献 [118,119] 考虑了其他不同的因子模型, 所有这些文献都依赖于数据的联合正态性假设, 但这在实际 应用中却难以保证. 最近, 文献 [81] 开发了一种带因子调节的稳健方法来处理重尾数据的 FDP 控制 问题.…”