Adaptive elastic-net selection in a quantile model with diverging number of variable groups

摘要

In real applications of the linear model, the explanatory variables are very often naturally grouped, the most common example being the multivariate variance analysis. In the present paper, a quantile model with group structure is considered, where the number of groups can diverge with the sample size. We introduce and study the adaptive elastic-net group quantile estimator, for improving the parameter estimation accuracy. This method allows automatic selection, with a probability converging to 1, of the non-zero coefficient vectors and further, the asymptotic normality of the non-zero parameter estimators. We also give the convergence rate of the adaptive elastic-net group quantile estimator, rate which depends on the number of the groups. In order to put the estimation method into practice, an algorithm based on the subgradient method is proposed and implemented. The performed Monte Carlo simulations show that the adaptive elastic-net group quantile estimations are more accurate than other existing group estimations in the literature. Moreover, the numerical study confirms the theoretical results and the usefulness of the proposed estimation method.