Weighted composite quantile regression for partially linear varying coefficient models

ABSTRACT

Partially linear varying coefficient models (PLVCMs) with heteroscedasticity are considered in this article. Based on composite quantile regression, we develop a weighted composite quantile regression (WCQR) to estimate the non parametric varying coefficient functions and the parametric regression coefficients. The WCQR is augmented using a data-driven weighting scheme. Moreover, the asymptotic normality of proposed estimators for both the parametric and non parametric parts are studied explicitly. In addition, by comparing the asymptotic relative efficiency theoretically and numerically, WCQR method all outperforms the CQR method and some other estimate methods. To achieve sparsity with high-dimensional covariates, we develop a variable selection procedure to select significant parametric components for the PLVCM and prove the method possessing the oracle property. Both simulations and data analysis are conducted to illustrate the finite-sample performance of the proposed methods.

KEYWORDS:

• Partially linear varying coefficient models
• Variable selection
• Weighted composite quantile regression.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 60G08
• Secondary: 62G20

Acknowledgments

The authors thank editors and referees for their constructive comments and variable suggestions which have greatly improved the article.

Additional information

Funding

This research is supported by National Natural Science Foundation of China (Series number: 11626057) for Rong Jiang. Additional partial support is also provided by the Fundamental Research Funds for the Central Universities of China (Series number: 17D110905) for Rong Jiang at Donghua University and Shanghai Sailing Program (Series number: 17YF1400800).