Efficient importance sampling imputation algorithms for quantile and composite quantile regression

Nowadays, missing data in regression model is one of the most well-known topics. In this paper, we propose a class of efficient importance sampling imputation algorithms (EIS) for quantile and composite quantile regression with missing covariates. They are an EIS in quantile regression (EISQ) and its three extensions in composite quantile regression (EISCQ). Our EISQ uses an interior point (IP) approach, while EISCQ algorithms use IP and other two well-known approaches: Majorize-minimization (MM) and coordinate descent (CD). The aims of our proposed EIS algorithms are to decrease estimated variances and relieve computational burden at the same time, which improves the performances of coefficients estimators in both estimated and computational efficiencies. To compare our EIS algorithms with other existing competitors including complete cases analysis and multiple imputation, the paper carries out a series of simulation studies with different sample sizes and different levels of missing rates under different missing mechanism models. Finally, we apply all the algorithms to part of the examination data in National Health and Nutrition Examination Survey.