Variable selection with group structure in competing risks quantile regression.

We study the group bridge and the adaptive group bridge penalties for competing risks quantile regression with group variables. While the group bridge consistently identifies nonzero group variables, the adaptive group bridge consistently selects variables not only at group level but also at within-group level. We allow the number of covariates to diverge as the sample size increases. The oracle property for both methods is also studied. The performance of the group bridge and the adaptive group bridge is compared in simulation and in a real data analysis. The simulation study shows that the adaptive group bridge selects nonzero within-group variables more consistently than the group bridge. A bone marrow transplant study is provided as an example.