Group penalized quantile regression

Mohamed Ouhourane (), Yi Yang (), Andréa L. Benedet () and Karim Oualkacha ()
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Mohamed Ouhourane: Université du Québec à Montréal
Yi Yang: McGill University
Andréa L. Benedet: McGill University Research Centre for Studies in Aging
Karim Oualkacha: Université du Québec à Montréal

Statistical Methods & Applications, 2022, vol. 31, issue 3, No 3, 495-529

Abstract: Abstract Quantile regression models have become a widely used statistical tool in genetics and in the omics fields because they can provide a rich description of the predictors’ effects on an outcome without imposing stringent parametric assumptions on the outcome-predictors relationship. This work considers the problem of selecting grouped variables in high-dimensional linear quantile regression models. We introduce a group penalized pseudo quantile regression (GPQR) framework with both group-lasso and group non-convex penalties. We approximate the quantile regression check function using a pseudo-quantile check function. Then, using the majorization–minimization principle, we derive a simple and computationally efficient group-wise descent algorithm to solve group penalized quantile regression. We establish the convergence rate property of our algorithm with the group-Lasso penalty and illustrate the GPQR approach performance using simulations in high-dimensional settings. Furthermore, we demonstrate the use of the GPQR method in a gene-based association analysis of data from the Alzheimer’s Disease Neuroimaging Initiative study and in an epigenetic analysis of DNA methylation data.

Keywords: Coordinate descent algorithm; Group penalized regression; Heterogeneous; Pseudo-quantile; Variable selection; Quantile regression (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10260-021-00580-8

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