This paper proposes a double penalized quantile regression for linear mixed effects model, which can select fixed and random effects simultaneously. Instead of using two tuning parameters, the proposed iterative algorithm enables only one optimal tuning parameter in each step and is more efficient. The authors establish asymptotic normality for the proposed estimators of quantile regression coefficients. Simulation studies show that the new method is robust to a variety of error distributions at different quantiles. It outperforms the traditional regression models under a wide array of simulat...
