Testing for marginal linear effects in quantile regression

Huixia Judy Wang, Ian W. McKeague, Min Qian

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

The paper develops a new marginal testing procedure to detect significant predictors that are associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then to base the test on the t-statistics that are associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behaviour due to the selection of the most predictive variables. Asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified. Even though a fixed dimension is assumed to derive the asymptotic results, the test proposed is applicable and computationally feasible for large dimensional predictors. The method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response. The approach is illustrated by using an application to a human immunodeficiency virus drug resistance data set.
Original languageEnglish (US)
Pages (from-to)433-452
Number of pages20
JournalJournal of the Royal Statistical Society: Series B (Statistical Methodology)
Volume80
Issue number2
DOIs
StatePublished - Oct 23 2017
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-2015-CRG4-2582
Acknowledgements: The research is partly supported by National Science Foundation grants DMS-1149355, DMS-1307838 and DMS-1712760, National Institutes of Health grants 2R01GM095722 and R21MH108999 and grant OSR-2015-CRG4-2582 from King Abdullah University of Science and Technology. The authors thank the Joint Editor, Associate Editor and three referees for their constructive comments and suggestions.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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