Robust estimation and variable selection for semiparametric partially linear varying coefficient model based on modal regression

Abstract

The semiparametric partially linear varying coefficient models (SPLVCM) are frequently used in statistical modelling, but most existing methods were built on either the least-square or likelihood-based methods, which are very sensitive to the outliers and their efficiency may be significantly reduced for heavy tail error distribution. This paper proposes a new efficient and robust estimation procedure for the SPLVCM based on modal regression. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts, and show that the estimators achieve the best convergence rate. Moreover, we develop a variable selection procedure to select significant parametric components for the SPLVCM and prove the method possessing the oracle property. We also discuss the bandwidth selection and propose an expectation-maximisation-type algorithm for the proposed estimation procedure. Some simulation results and real data analysis confirm that the newly proposed method works very competitively compared to other existing methods.