Variable Selection for Partially Linear Additive Model Based on Modal Regression Under High Dimensional Data

Abstract

In this article, we focus on the variable selection for partially linear additive model under high dimensional data. Variable selection is proposed based on modal regression estimation with Adoptive Bridge Method. Using the B-spline basic function to approximate the additive function, a penalty estimation objective equation is constructed. It establishes and proves that the variable selection methods have oracle property. Numerical simulations tested the performance of the proposed methods in a finite sample and verified the significance of the proposed estimation and the variable selection methods. At the end of the article, we attach the detailed derivation of the theoretical results. Therefore, the correctness of the method used is verified theoretically and practically.