Rate Optimal Estimation and Confidence Intervals for High-dimensional Regression with Missing Covariates
Rate Optimal Estimation and Confidence Intervals for High-dimensional Regression with Missing Covariates
复制标题
DOI：
10.1016/j.jmva.2019.06.004
复制
发表时间：
2017-02
期刊：
影响因子：
--
通讯作者：
Yining Wang;Jialei Wang;Sivaraman Balakrishnan;Aarti Singh
中科院分区：
文献类型：
--
作者：
Yining Wang;Jialei Wang;Sivaraman Balakrishnan;Aarti Singh
本文研究了稀疏高维线性回归模型中设计矩阵的协变量完全随机缺失时的估计和构造置信区间的问题。我们分析了一个变体的Dantzig选择器估计回归模型，我们使用去偏参数来构建组件的置信区间。我们还通过对合成和半合成数据的广泛模拟来补充材料中的数学研究，这些数据显示了我们对有限样本量的渐近预测的准确性。
We consider the problems of estimation and of constructing component-wise confidence intervals in a sparse high-dimensional linear regression model when some covariates of the design matrix are missing completely at random. We analyze a variant of the Dantzig selector for estimating the regression model and we use a de-biasing argument to construct component-wise confidence intervals. We also complement our mathematical study in the supplementary materials with extensive simulations on synthetic and semi-synthetic data that show the accuracy of our asymptotic predictions for finite sample sizes.