  We propose a general adaptive LASSO method for a quantile regression model.
Our method is very interesting when we know nothing about the first two moments
of the model error. We first prove that the obtained estimators satisfy the
oracle properties, which involves the relevant variable selection without using
hypothesis test. Next, we study the proposed method when the (multiphase) model
changes to unknown observations called change-points. Convergence rates of the
change-points and of the regression parameters estimators in each phase are
found. The sparsity of the adaptive LASSO quantile estimators of the regression
parameters is not affected by the change-points estimation. If the phases
number is unknown, a consistent criterion is proposed. Numerical studies by
Monte Carlo simulations show the performance of the proposed method, compared
to other existing methods in the literature, for models with a single phase or
for multiphase models. The adaptive LASSO quantile method performs better than
known variable selection methods, as the least squared method with adaptive
LASSO penalty, $L_1$-method with LASSO-type penalty and quantile method with
SCAD penalty.
