Quantile regression for robust estimation and variable selection in partially linear varying-coefficient models

ABSTRACT

In this paper, we develop a new estimation procedure based on quantile regression for semiparametric partially linear varying-coefficient models. The proposed estimation approach is empirically shown to be much more efficient than the popular least squares estimation method for non-normal error distributions, and almost not lose any efficiency for normal errors. Asymptotic normalities of the proposed estimators for both the parametric and nonparametric parts are established. To achieve sparsity when there exist irrelevant variables in the model, two variable selection procedures based on adaptive penalty are developed to select important parametric covariates as well as significant nonparametric functions. Moreover, both these two variable selection procedures are demonstrated to enjoy the oracle property under some regularity conditions. Some Monte Carlo simulations are conducted to assess the finite sample performance of the proposed estimators, and a real-data example is used to illustrate the application of the proposed methods.

KEYWORDS:

• Partially linear varying-coefficient models
• quantile regression
• robustness
• variable selection
• oracle property

AMS SUBJECT CLASSIFICATIONS:

• 62G08
• 62G05
• 62G20

Acknowledgements

The authors are grateful to the Editor, Associate Editor and two anonymous referees whose comments lead to a significant improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant number 11671059].