Rank regression estimation for dynamic single index varying coefficient models

Abstract

Rank regression has become increasingly popular for robust inference in statistics. However, there iss no research for the dynamic single index varying coefficient model (DSIVCM), and only the least squares method has been developed for DSIVCM up to now, which is very sensitive to outliers or violations of certain model assumptions. To address these issues, we propose the rank regression estimation method for DSIVCM based on B-splines approximations, which results in robust estimators of coefficient functions for this general class of models. In addition, we develop a practical algorithm for computation and provide a data-driven procedure to select the smoothing parameters. The theoretical properties of proposed estimators are established under some reasonable conditions. The utility of newly proposed method is investigated through simulation studies and a real-data example.