The paper concerns the regularized quantile regression for ultrahigh-dimensional data with responses missing not at random. The propensity score is specified by the semiparametric exponential tilting model. We use the Pearson Chi-square type test statistic for identification of the important features in the sparse propensity score model, and employ the adjusted empirical likelihood method for estimation of the parameters in the reduced model. With the estimated propensity score model, we suggest an inverse probability weighted and penalized objective function for regularized estimation using the nonconvex SCAD penalty and MCP functions. Assuming the propensity score model is of low dimension, we establish the oracle properties of the proposed regularized estimators. The new method has several desirable advantages. First, it is robust to heavy-tailed errors or potential outliers in the responses. Second, it can accommodate nonignorable nonresponse data. Third, it can deal with ultrahigh-dimensional data with heterogeneity. Simulation study and real data analysis are given to examine the finite sample performance of the proposed approaches.

中文翻译：

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具有不可忽略的缺失响应的超高维数据的正则化分位数回归

该论文涉及响应非随机缺失的超高维数据的正则化分位数回归。倾向得分由半参数指数倾斜模型指定。我们使用 Pearson 卡方类型检验统计量来识别稀疏倾向评分模型中的重要特征，并使用调整后的经验似然方法来估计简化模型中的参数。使用估计的倾向得分模型，我们建议使用非凸 SCAD 惩罚和 MCP 函数进行正则化估计的逆概率加权和惩罚目标函数。假设倾向评分模型是低维的，我们建立了所提出的正则化估计器的预言机属性。新方法有几个理想的优点。第一的，它对响应中的重尾错误或潜在异常值具有鲁棒性。其次，它可以容纳不可忽略的无响应数据。第三，它可以处理具有异质性的超高维数据。给出了仿真研究和实际数据分析，以检验所提出方法的有限样本性能。