Journal of Mathematics and Statistics


Yanan Hu, Qianqian Zhu and Maozai Tian

DOI : 10.3844/jmssp.2014.30.44

Journal of Mathematics and Statistics

Volume 10, Issue 1

Pages 30-44


In this study, we consider the nonparametric quantile regression model with the covariates Missing at Random (MAR). Multiple imputation is becoming an increasingly popular approach for analyzing missing data, which combined with quantile regression is not well-developed. We propose an effective and accurate two-stage multiple imputation method for the model based on the quantile regression, which consists of initial imputation in the first stage and multiple imputation in the second stage. The estimation procedure makes full use of the entire dataset to achieve increased efficiency and we show the proposed two-stage multiple imputation estimator to be asymptotically normal. In simulation study, we compare the performance of the proposed imputation estimator with Complete Case (CC) estimator and other imputation estimators, e.g., the regression imputation estimator and k-Nearest-Neighbor imputation estimator. We conclude that the proposed estimator is robust to the initial imputation and illustrates more desirable performance than other comparative methods. We also apply the proposed multiple imputation method to an AIDS clinical trial data set to show its practical application.


© 2014 Yanan Hu, Qianqian Zhu and Maozai Tian. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.