  In this paper we are interested in parameters estimation of linear model when
number of parameters increases with sample size. Without any assumption about
moments of the model error, we propose and study the seamless $L_0$ quantile
estimator. For this estimator we first give the convergence rate. Afterwards,
we prove that it correctly distinguishes between zero and nonzero parameters
and that the estimators of the nonzero parameters are asymptotically normal. A
consistent BIC criterion to select the tuning parameters is given.
