Variable Selection For Semiparametric Varying Coefficient Models With Heredity Constraint

This paper mainly studies the variable selection and model estimation of semiparametric varying coefficient model with heredity constraint.As a special case of the varying coefficient model,the semiparametric varying coefficient model not only retains the easy interpretability of the linear model,but also has the flexibility of the nonparametric model.This paper not only pays attention to the influence of the independent variable itself on the response variable,but also focuses on the influence of the interaction between variables on the response variable,and the interaction term satisfies the heredity constraint,that is,the interaction term exists only when the main effect exists.we simultaneously perform coefficient estimation and variable selection by combining kernel estimation method,SCAD penalty and Group SCAD penalty.Under some certain regular conditions,the consistency of model selection and asymptotic normality of parameter estimation are established;by choosing an appropriate binwidth and penalized parameters,the nonparametric part can achieve the optimal convergence speed.Numerical simulation studies show that the method proposed in this paper can perform well in coefficient estimation and variable selection in the case of finite samples.