In this paper, we discuss the quantile regression and variable selection of partially linear single-index model when data are missing at random, which allows the response and covariates missing simultaneously. By using iteration algorithm and local linear method, we construct the inverse probability weighted quantile estimators of both the parameters and the link function. The penalized estimator of the parameters is also considered based on the adaptive LASSO penalty. The asymptotic distributions and the oracle property of the proposed estimators are derived. Simulation study and real data analysis are presented to show the performance of the proposed methods.

中文翻译：

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缺少观测值的部分线性单指标模型的分位数回归

在本文中，我们讨论了随机丢失数据时部分线性单指标模型的分位数回归和变量选择，该模型允许响应和协变量同时丢失。通过使用迭代算法和局部线性方法，我们构造了参数和链接函数的逆概率加权分位数估计量。还基于自适应LASSO罚分考虑参数的惩罚估计量。推导了估计量的渐近分布和oracle性质。仿真研究和实际数据分析表明了所提出方法的性能。