Model detection and variable selection for mode varying coefficient model

Varying coefficient model is often used in statistical modeling since it is more flexible than the parametric model. However, model detection and variable selection of varying coefficient model are poorly understood in mode regression. Existing methods in the literature for these problems are often based on mean regression and quantile regression. In this paper, we propose a novel method to solve these problems for mode varying coefficient model based on the B-spline approximation and SCAD penalty. Moreover, we present a new algorithm to estimate the parameters of interest, and discuss the parameters selection for the tuning parameters and bandwidth. We also establish the asymptotic properties of estimated coefficients under some regular conditions. Finally, we illustrate the proposed method by some simulation studies and an empirical example.