Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, China.
School of Statistics and Information, Xinjiang University of Finance and Economics, Urumqi, China.
Stat Methods Med Res. 2021 Jan;30(1):129-150. doi: 10.1177/0962280220941533. Epub 2020 Aug 3.
In this paper, we consider variable selection for ultra-high dimensional quantile regression model with missing data and measurement errors in covariates. Specifically, we correct the bias in the loss function caused by measurement error by applying the orthogonal quantile regression approach and remove the bias caused by missing data using the inverse probability weighting. A nonconvex Atan penalized estimation method is proposed for simultaneous variable selection and estimation. With the proper choice of the regularization parameter and under some relaxed conditions, we show that the proposed estimate enjoys the oracle properties. The choice of smoothing parameters is also discussed. The performance of the proposed variable selection procedure is assessed by Monte Carlo simulation studies. We further demonstrate the proposed procedure with a breast cancer data set.
在本文中，我们考虑了具有缺失数据和协变量测量误差的超高维分位数回归模型的变量选择。具体来说，我们通过应用正交分位数回归方法来纠正由测量误差引起的损失函数中的偏差，并通过逆概率加权来消除由缺失数据引起的偏差。我们提出了一种非凸 Atan 惩罚估计方法，用于同时进行变量选择和估计。通过适当选择正则化参数并在一些放宽的条件下，我们证明了所提出的估计具有 Oracle 属性。还讨论了平滑参数的选择。通过蒙特卡罗模拟研究评估了所提出的变量选择过程的性能。我们进一步使用乳腺癌数据集来说明所提出的程序。
