  The paper considers a linear regression model in high-dimension for which the
predictive variables can change the influence on the response variable at
unknown times (called change-points). Moreover, the particular case of the
heavy-tailed errors is considered. In this case, least square method with LASSO
or adaptive LASSO penalty can not be used since the theoretical assumptions do
not occur or the estimators are not robust. Then, the quantile model with SCAD
penalty or median regression with LASSO-type penalty allows, in the same time,
to estimate the parameters on every segment and eliminate the irrelevant
variables. We show that, for the two penalized estimation methods, the oracle
properties is not affected by the change-point estimation. Convergence rates of
the estimators for the change-points and for the regression parameters, by the
two methods are found. Monte-Carlo simulations illustrate the performance of
the methods.
