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2016 Familywise error rate control via knockoffs
Lucas Janson, Weijie Su
Electron. J. Statist. 10(1): 960-975 (2016). DOI: 10.1214/16-EJS1129

Abstract

We present a novel method for controlling the $k$-familywise error rate ($k$-FWER) in the linear regression setting using the knockoffs framework first introduced by Barber and Candès. Our procedure, which we also refer to as knockoffs, can be applied with any design matrix with at least as many observations as variables, and does not require knowing the noise variance. Unlike other multiple testing procedures which act directly on $p$-values, knockoffs is specifically tailored to linear regression and implicitly accounts for the statistical relationships between hypothesis tests of different coefficients. We prove that knockoffs controls the $k$-FWER exactly in finite samples and show in simulations that it provides superior power to alternative procedures over a range of linear regression problems. We also discuss extensions to controlling other Type I error rates such as the false exceedance rate, and use it to identify candidates for mutations conferring drug-resistance in HIV.

Citation

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Lucas Janson. Weijie Su. "Familywise error rate control via knockoffs." Electron. J. Statist. 10 (1) 960 - 975, 2016. https://doi.org/10.1214/16-EJS1129

Information

Received: 1 October 2015; Published: 2016
First available in Project Euclid: 12 April 2016

zbMATH: 1341.62245
MathSciNet: MR3486422
Digital Object Identifier: 10.1214/16-EJS1129

Subjects:
Primary: 62F03, 62J15
Secondary: 62J05

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 1 • 2016
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