Model detection and variable selection for mode varying coefficient model

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