Estimation in partial linear model with spline modal function

Abstract

Semiparametric partial linear models are often used in real data analysis for their flexibility and parsimony. A well-known example of semiparametric partial linear models is the partially linear varying coefficient model. Statistical inference of this model is restricted to a condition that the components of varying and constant coefficients are known in advance. However, in practice, this is not known which subset of variables have constant or varying effect on the response. Therefore, it is of great interest to develop some efficient methods to distinguish constant components from varying ones. In this article, we propose a robust method for simultaneously structure identification and variable selection in varying coefficient models based on modal regression, which is robust with respect to non-normal errors and outliers in the response. The proposed procedure can achieve robustness and efficiency by using a bandwidth parameter. The performance of the proposed method is examined by a simulation study and real data analysis to show its capabilities when the error distribution is varied.