The conditional permutation test for independence while controlling for confounders

Thomas B. Berrett, Yi Wang, Rina Foygel Barber and Richard J. Samworth

Journal of the Royal Statistical Society Series B, 2020, vol. 82, issue 1, 175-197

Abstract: We propose a general new method, the conditional permutation test, for testing the conditional independence of variables X and Y given a potentially high dimensional random vector Z that may contain confounding factors. The test permutes entries of X non‐uniformly, to respect the existing dependence between X and Z and thus to account for the presence of these confounders. Like the conditional randomization test of Candès and co‐workers in 2018, our test relies on the availability of an approximation to the distribution of X|Z—whereas their test uses this estimate to draw new X‐values, for our test we use this approximation to design an appropriate non‐uniform distribution on permutations of the X‐values already seen in the true data. We provide an efficient Markov chain Monte Carlo sampler for the implementation of our method and establish bounds on the type I error in terms of the error in the approximation of the conditional distribution of X|Z, finding that, for the worst‐case test statistic, the inflation in type I error of the conditional permutation test is no larger than that of the conditional randomization test. We validate these theoretical results with experiments on simulated data and on the Capital Bikeshare data set.

Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://doi.org/10.1111/rssb.12340

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:82:y:2020:i:1:p:175-197

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().