  Sparse group LASSO (SGL) is a penalization technique used in regression
problems where the covariates have a natural grouped structure and provides
solutions that are both between and within group sparse. In this paper the SGL
is introduced to the quantile regression (QR) framework, and a more flexible
version, the adaptive sparse group LASSO (ASGL), is proposed. This proposal
adds weights to the penalization improving prediction accuracy. Usually,
adaptive weights are taken as a function of the original nonpenalized solution
model. This approach is only feasible in the n > p framework. In this work, a
solution that allows using adaptive weights in high-dimensional scenarios is
proposed. The benefits of this proposal are studied both in synthetic and real
datasets.
