Robust estimation and outlier detection for varying-coefficient models via penalized regression

Abstract

Varying-coefficient models (VCMs) are widely used in a variety of statistical applications. However, the classical VCMs based on least squares are prone to the presence of even a few severe outliers. In this article, a mean shift parameter is added for each observation to reflect outliers, and different penalties are then applied to the shift parameters to get sparse estimates. The jointly penalized optimization problem is solved through an efficient algorithm, and the tuning parameters are chosen by the Bayesian information criteria (BIC). The efficiency of the new approach is demonstrated via simulation studies as well as a real application on the Hong Kong environmental data.

KEYWORDS:

• Outlier detection
• Penalized regression
• Varying-coefficient models

Acknowledgements

The authors are grateful to the editor, the associate editor, and one referee for the numerous helpful comments during the preparation of the article.

Additional information

Funding

Yang’s research was supported by the National Nature Science Foundation of China grant 11871173, the National Social Science Foundation of China grant 16BTJ032, the Guangdong Province Nature Science Foundation of China grants 2019A1515010721 and the Fundamental Research Funds for the Central University 19JNYH08. Xu’s research is supported by Zhejiang Provincial NSF of China grant LY19A010006, and the First Class Discipline of Zhejiang-A (Zhejiang University of Finance and Economics- Statistics). Yao’s research is supported by NSF grant DMS-1461677 and Department of Energy with the award No: 10006272. Xiang’s research is supported by the First Class Discipline of Zhejiang-A (Zhejiang University of Finance and Economics- Statistics).