We consider model selection via \(\ell _0\) -penalty for high-dimensional sparse quantile regression models. This procedure is almost equivalent to model selection via information criterion due to similarity in penalty. We deal with linear models, additive models, and varying coefficient models in a unified way and establish the model selection consistency results rigorously when the size of the relevant index set goes to infinity. The treatment of this situation is challenging and the theoretical novelty of our results is important because such information criteria are commonly used. We consider two different setups and propose tuning parameters in the \(\ell _0\) -penalty. Besides, we propose a feasible algorithm for computation of our estimator and the numerical study results are presented.
