Adaptive elastic-net and fused estimators in high-dimensional group quantile linear model
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In applications, the variables are naturally grouped in a linear quantile model, the most common example being the multivariate variance analysis. For this model, with the possibility that the number of groups diverges with sample size, we introduce and study the adaptive elastic-net estimation method. This method automatically selects, with a probability converging to one, the significant groups and, moreover, the non zero parameter estimators are asymptotically normal. The Monte Carlo simulations, using a subgradient proposed algorithm, show that the adaptive elastic-net group quantile estimations are more accurate that other existing group estimations in the literature. When the number of groups coincides whit the number of observations, a fused penalty allows automatically detection of consecutive groups which have the same influence on the response variable. We obtain an upper bound of the number of the consecutive groups with different estimators.
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