Adaptive sparse group LASSO in quantile regression

This paper studies the introduction of sparse group LASSO (SGL) to the quantileregression framework. Additionally, a more flexible version, an adaptive SGL isproposed based on the adaptive idea, this is, the usage of adaptive weights in the penalization. Adaptive estimators are usually focused on the study of the oracle propertyunder asymptotic and double asymptotic frameworks. A key step on the demonstration of this property is to consider adaptive weights based on a initial √n-consistentestimator. In practice this implies the usage of a non penalized estimator that limitsthe adaptive solutions to low dimensional scenarios. In this work, several solutions,based on dimension reduction techniques PCA and PLS, are studied for the calculationof these weights in high dimensional frameworks. The benefits of this proposal arestudied both in synthetic and real datasets.

Adaptive sparse group LASSO in quantile regression Articles