Robust modal estimation and variable selection for single-index varying-coefficient models

ABSTRACT

In this article, we present a new efficient iteration estimation approach based on local modal regression for single-index varying-coefficient models. The resulted estimators are shown to be robust with regardless of outliers and error distributions. The asymptotic properties of the estimators are established under some regularity conditions and a practical modified EM algorithm is proposed for the new method. Moreover, to achieve sparse estimator when there exists irrelevant variables in the index parameters, a variable selection procedure based on SCAD penalty is developed to select significant parametric covariates and the well-known oracle properties are also derived. Finally, some numerical examples with various distributed errors and a real data analysis are conducted to illustrate the validity and feasibility of our proposed method.

KEYWORDS:

• Local modal regression
• Oracle property
• Robustness
• Single-index varying-coefficient model
• Variable selection

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08
• 62G05
• 62G20

Acknowledgments

The author is grateful to the Editor and two anonymous referees whose comments lead to a significant improvement of the article. This research was supported by the National Natural Science Foundation of China (Grant No. 11171361) and Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20110191110033).