Covariate powered cross‐weighted multiple testing

Nikolaos Ignatiadis and Wolfgang Huber

Journal of the Royal Statistical Society Series B, 2021, vol. 83, issue 4, 720-751

Abstract: A fundamental task in the analysis of data sets with many variables is screening for associations. This can be cast as a multiple testing task, where the objective is achieving high detection power while controlling type I error. We consider m hypothesis tests represented by pairs ((Pi,Xi))1≤i≤m of p‐values Pi and covariates Xi, such that Pi⊥Xi if Hi is null. Here, we show how to use information potentially available in the covariates about heterogeneities among hypotheses to increase power compared to conventional procedures that only use the Pi. To this end, we upgrade existing weighted multiple testing procedures through the independent hypothesis weighting (IHW) framework to use data‐driven weights that are calculated as a function of the covariates. Finite sample guarantees, for example false discovery rate control, are derived from cross‐weighting, a data‐splitting approach that enables learning the weight‐covariate function without overfitting as long as the hypotheses can be partitioned into independent folds, with arbitrary within‐fold dependence. IHW has increased power compared to methods that do not use covariate information. A key implication of IHW is that hypothesis rejection in common multiple testing setups should not proceed according to the ranking of the p‐values, but by an alternative ranking implied by the covariate‐weighted p‐values.

Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/rssb.12411

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:83:y:2021:i:4:p:720-751

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 ().