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Group penalized quantile regression

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohamed Ouhourane & Yi Yang & Andréa L. Benedet & Karim Oualkacha, 2022. "Group penalized quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 495-529, September.
    • Handle: RePEc:spr:stmapp:v:31:y:2022:i:3:d:10.1007_s10260-021-00580-8
    DOI: 10.1007/s10260-021-00580-8
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    References listed on IDEAS

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