A resampling method by perturbing the estimating functions for quantile regression with missing data

ABSTRACT

In this article, we propose a resampling method based on perturbing the estimating functions to compute the asymptotic variances of quantile regression estimators under missing at random condition. We prove that the conditional distributions of the resampling estimators are asymptotically equivalent to the distributions of quantile regression estimators. Our method can deal with complex situations, where the response and part of covariates are missing. Numerical results based on simulated and real data are provided under several designs.

KEYWORDS:

• Bootstrap
• Estimating equations
• Missing data
• Resampling method
• Quantile regression

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G09

Acknowledgements

Zhou’s work was supported by National Natural Science Foundation of China (NSFC) (71271128), the State Key Program of National Natural Science Foundation of China (71331006), the State Key Program in the Major Research Plan of National Natural Science Foundation of China (91546202), National Center for Mathematics and Interdisciplinary Sciences (NCMIS), Key Laboratory of RCSDS, AMSS, CAS (2008DP173182) and Innovative Research Team of Shanghai University of Finance and Economics (IRTSHUFE13122402), Program for Changjiang Scholars Innovative Research Team of Ministry of Education (IRT13077). Zhang’s work was supported by National Natural Science Foundation of China (NSFC)(11601424), Youth Foundation of the Ministry of Education of China (15YJC910009), Science Foundation of Northwest University (14NW31).