Estimation for the censored partially linear quantile regression models

ABSTRACT

In this article, we develop estimation procedures for partially linear quantile regression models, where some of the responses are censored by another random variable. The nonparametric function is estimated by basis function approximations. The estimation procedure is easy to implement through existing weighted quantile regression, and it requires no specification of the error distributions. We show the large-sample properties of the resulting estimates, the proposed estimator of the regression parameter is root-n consistent and asymptotically normal and the estimator of the functional component achieves the optimal convergence rate of the nonparametric function. The proposed method is studied via simulations and illustrated with the analysis of a primary biliary cirrhosis (BPC) data.

KEYWORDS:

• K-M estimator
• Partially linear regression models
• Quantile regression
• Random censoring

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 62G20

Additional information

Funding

Du’s work is supported by the National Natural Science Foundation of China (No. 11501018, No. 11571340), Program for Rixin Talents in Beijing University of Technology, and the Science and Technology Project of Beijing Municipal Education Commission (KM201710005032). Zhang’s work is partly supported by the National Natural Science Foundation of China (No. 11271039), and Education Ministry Funds for Doctor Supervisors. Xu’s work is supported by the Zhejiang Provincial Natural Science Foundation of China (LY17A010026), National Natural Science Foundation of China (11301485), and Startup Foundation for Talents in Zhejiang Agriculture and Forestry University (2016FR030).