  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 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.
