Variable selection for mode regression

From the prediction viewpoint, mode regression is more attractive since it pay attention to the most probable value of response variable given regressors. On the other hand, high-dimensional data are very prevalent as the advance of the technology of collecting and storing data. Variable selection is an important strategy to deal with high-dimensional regression problem. This paper aims to propose a variable selection procedure for high-dimensional mode regression via combining nonparametric kernel estimation method with sparsity penalty tactics. We also establish the asymptotic properties under certain technical conditions. The effectiveness and flexibility of the proposed methods are further illustrated by numerical studies and the real data application.