Imputation in nonparametric quantile regression with complex data

This paper considers nonparametric quantile regression models for complex data of mixed categorical and continuous variables together with missing values at random (MAR). In consideration of the increasingly popular application of multiple imputation for handling missing data and the advantages of nonparametric quantile regression, we propose an effective and accurate multiple imputation method. The estimation procedure not only does well in modeling with mixed categorical and continuous data, but also makes full use of the entire data set to achieve increased efficiency. The proposed estimator is asymptotically normal. In simulation study, we compare the performance of the multiple imputation method with complete case (CC), Regression imputation and nearest-neighbor imputation methods, and outline advantages and drawbacks of the different methods. Simulation studies show that the proposed multiple imputation method performs better.