Robust estimation for partial linear single-index models

Abstract

In this article, minimum average variance estimation (MAVE) based on local modal regression is proposed for partial linear single-index models, which can be robust to different error distributions or outliers. Asymptotic distributions of the proposed estimators are derived, which have the same convergence rate as the original MAVE based on least squares. A modal EM algorithm is provided to implement our robust estimation. Both simulation studies and a real data example are used to evaluate the finite sample performance of the proposed estimation procedure.

Keywords:

• Partial linear single-index model
• modal regression
• MAVE
• robust estimation
• asymptotic properties

Acknowledgments

The authors are grateful to the editor, associate editor and two anonymous referees for their thoughtful and constructive comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Yang Zhao's research was supported by the National Natural Science Foundation of China [grant number 12061044]. Sanying Feng's research was supported by the Humanities and Social Science Project of Ministry of Education of China [grant number 21YJC910003], the Natural Science Foundation of Henan Province, China [grant number 212300410412], the Foundation of Henan Educational Committee, China [grant number 21A910004].