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In real applications of the linear model, the explanatory variables are veryoften naturally grouped, the most common example being the multivariatevariance analysis. In the present paper, a quantile model with structure groupis considered, the number of groups can diverge with sample size. We introduceand study the adaptive elastic-net group estimator, for improving the parameterestimation accuracy. This method allows automatic selection, with a probabilityconverging to one, of significant groups and further the non zero parameterestimators are asymptotically normal. The convergence rate of the adaptiveelastic-net group quantile estimator is also obtained, rate which depends onthe number of groups. In order to put the estimation method into practice, analgorithm based on the subgradient method is proposed and implemented. TheMonte Carlo simulations show that the adaptive elastic-net group quantileestimations are more accurate that other existing group estimations in theliterature. Moreover, the numerical study confirms the theoretical results andthe usefulness of the proposed estimation method.

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