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.

Keywords:

• Dynamic single index varying coefficient model
• rank regression
• B-splines
• robust estimation
• convergence rate

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the University Social Science Research Project of Anhui Province (SK2020A0051), the Anhui Provincial Philosophy and Social Science Project (AHSKF2022D08) and the Natural Science Foundation of Education Department of Anhui Province (2022AH050599).