Penalized empirical likelihood based variable selection for partially linear quantile regression models with missing responses

In this paper, we consider variable selection for partially linear quantile regression models with missing response at random. We first propose a role penalized empirical likelihood based variable selection method, and show that such variable selection method is consistent and satisfi es sparsity. Further more, to avoid the influence of nonparametric estimator on the variable selection for the parametric components, we also propose a double penalized empirical likelihood variable selection method. Some simulation studies and a real data application are under taken to assess the finite sample performance of the proposed variable selection methods, and simulation results indicate that the proposed variable selection methods are workable.