Statistics Papers

Document Type

Journal Article

Date of this Version

2016

Publication Source

Electronic Journal of Statistics

Volume

10

Issue

1

Start Page

960

Last Page

975

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.

Copyright/Permission Statement

The original and published work is available at: https://projecteuclid.org/euclid.ejs/1460463651#abstract

Keywords

k-familywise error rate, knockoffs, multiple testing, linear regression, Lasso, negative binomial distribution

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Date Posted: 27 November 2017

This document has been peer reviewed.