Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. 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 [9] for estimating the regression model and we use a de-biasing argument to construct component-wise confidence intervals. Our first main result is to establish upper bounds on the estimation error as a function of the model parameters (the sparsity level s, the expected fraction of observed covariates $ρ_*$, and a measure of the signal strength $\|β^*\|_2$). We find that even in an idealized setting where the covariates are assumed to be missing completely at random, somewhat surprisingly and in contrast to the fully-observed setting, there is a dichotomy in the dependence on model parameters and much faster rates are obtained if the covariance matrix of the random design is known. To study this issue further, our second main contribution is to provide lower bounds on the estimation error showing that this discrepancy in rates is unavoidable in a minimax sense. We then consider the problem of high-dimensional inference in the presence of missing data. We construct and analyze confidence intervals using a de-biased estimator. In the presence of missing data, inference is complicated by the fact that the de-biasing matrix is correlated with the pilot estimator and this necessitates the design of a new estimator and a novel analysis. We also complement our mathematical study with extensive simulations on synthetic and semi-synthetic data that show the accuracy of our asymptotic predictions for finite sample sizes.
Doubly robust target inference for generalized linear regression with completely missing covariates
School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）；Department of Statistics and Data Science, Tsinghua University（清华大学统计与数据科学系）
Doubly Robust Machine Learning for Population Size Estimation with Missing Covariates: Application to Gaza Conflict Mortality
Center for Data Science New York University（纽约大学数据科学中心）；Department of Statistics & Data Science Carnegie Mellon University（卡内基梅隆大学统计与数据科学系）；Department of Medical Statistics London School of Hygiene and Tropical Medicine（伦敦卫生与热带医学院医学统计学系）
Minimum Wasserstein distance estimator under covariate shift: closed-form, super-efficiency and irregularity
KLATASDS-MOE, School of Statistics, East China Normal University（华东师范大学统计学院）；Institute of Statistics and Big Data, Renmin University of China（中国人民大学统计与大数据研究院）
Confidence intervals for high-dimensional Cox models
在协变量数可能大于样本量的高维Cox比例风险回归模型中，构造回归系数的置信区间。我们的去偏估计量构造类似于Zhang and Zhang（2014）和van de Geer et al.（2014），但时间相关协变量和删失风险集引入了相当多的额外挑战。我们的理论结果，这提供了条件下，我们的置信区间是渐近有效的，支持广泛的数值实验。
kNN estimation in semi-functional partial linear regression with missing responses at random
Universidade da Coruña（拉科鲁尼亚大学）；Centro de Investigación en Tecnologías de la Información y las Comunicaciones (CITIC)（信息与通信技术研究中心）；Universidad Carlos III de Madrid（马德里卡洛斯三世大学）
Statistical Laboratory, University of Cambridge（剑桥大学统计实验室）；Department of Data Sciences and Operations, University of Southern California（南加州大学数据科学与操作系）；Department of Statistics, University of Chicago（芝加哥大学统计学系）
Valid Post-selection Inference in Assumption-lean Linear Regression
基于数据驱动选择的估计量有效统计推断的构造近年来受到了广泛关注。Berk等人（2013）可能是第一个在任意协变量/变量选择下为具有固定协变量的高斯同方差线性回归提供有效推断的工作。该设置是不现实的，Bachoc et al.（2016）通过放松分布假设进行了扩展。上述工作的一个主要缺点是有效置信区域的构造是计算密集的。本文首先证明了后选择推理等价于同时推理，然后构造了计算简单的有效后选择置信区域。我们的构造是基于确定性不等式和适用于独立以及相关的随机变量，而不需要正确的分布假设。最后，我们比较了我们的置信区域与现有的体积，并表明在非随机协变量，我们的区域要小得多。
Augmented transfer regression learning for completely missing covariates
School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）；Department of Statistics, Colorado State University（科罗拉多州立大学统计学系）
Propensity score estimation using classification and regression trees in the presence of missing covariate data
Leiden University Medical Center（莱顿大学医学中心）
数据挖掘和机器学习技术，如分类和回归树（CART）代表了一个有前途的替代传统的逻辑斯谛回归的倾向得分估计。尽管不完整的数据排除了对所有受试者进行逻辑斯谛回归的拟合，但CART之所以吸引人，部分原因是某些实现允许将不完整的记录并入树拟合中，并为所有受试者提供倾向得分估计。基于理论上的考虑，我们认为，自动处理缺失数据的CART可能是不合适的。使用一系列模拟实验，我们检查了不同方法处理缺失协变量数据的性能;（i）将CART算法直接应用于（部分）不完整的数据，（ii）完整的案例分析，（iii）多重插补。评估了评估确认-结局效应\add{among the exposed}的偏倚、标准误、均方误差和覆盖率。将CART算法直接应用于不完整的数据会导致偏倚，即使在数据完全随机完全随机缺失的情况下也是如此。总体而言，多重插补后加CART的结果最佳。我们的研究表明，在CART中自动处理缺失数据可能会导致严重偏倚，并且作为解释缺失数据的一种手段，其性能并不优于多重插补。
