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 (EIS_Q) and its three extensions in composite quantile regression (EIS_CQ). Our EIS_Q uses an interior point (IP) approach, while EIS_CQ 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.

中文翻译：

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用于分位数和复合分位数回归的有效重要性采样插补算法

如今，回归模型中的缺失数据是最知名的话题之一。在本文中，我们提出了一类有效的重要性采样插补算法（EIS），用于缺少协变量的分位数和复合分位数回归。它们是分位数回归中的 EIS (EIS _Q ) 及其在复合分位数回归 (EIS _CQ ) 中的三个扩展。我们的 EIS _Q使用内点 (IP) 方法，而 EIS _CQ算法使用 IP 和其他两种众所周知的方法：Majorize-minimization (MM) 和坐标下降 (CD)。我们提出的 EIS 算法的目的是减少估计方差并同时减轻计算负担，从而提高系数估计器在估计效率和计算效率方面的性能。为了将我们的 EIS 算法与其他现有竞争对手（包括完整案例分析和多重插补）进行比较，本文在不同缺失机制模型下对不同样本量和不同缺失率水平进行了一系列模拟研究。最后，我们将所有算法应用于国民健康和营养调查中的部分检查数据。