Abstract: A unified variable selection invarying coefficient model with modal regressionis studied. B spline basis function is adopted to approximate the nonparametric part, and SCAD penalty function is established under modal regression. The proposed procedure using SCAD penalty function to select important variables simultaneously for the varying coefficient model can also identify the covariates with constant effects. Under certain conditions, the concoherence and sparseness of penalty estimation are proved. Finally, the effectiveness of the proposed variable selection method is evaluated by numerical simulation.

Key words: Modal regression, varying coefficient model, variable selection, SCAD penalty