数据带污染现象是制约高维统计推断的重要瓶颈之一，此时标准的正则化方法如Lasso将产生不稳定、有偏甚至错误的结果。本项目旨在高维变系数部分线性模型下，针对参数部分协变量带有测量误差和随机缺失两种污染情形，提出统一的矫正方案并进行理论分析。第一，将两类污染的模型整合到同一个可加误差模型框架下，进而利用正交投影方法将新模型转换成高维线性模型进行研究；第二，针对正态和非正态模型误差，分别基于偏差矫正的加权最小二乘Lasso和加权分位数Lasso方法对参数模型进行稀疏推断，其中我们将利用凸条件Lasso和锥规划等技巧对非凸的正则化目标函数进行凸化处理；第三，在常见的稀疏性假设下建立新方法模型选择的相合性，并借助各类范数建立估计误差的上界。我们的方法适用于高维/超高维稀疏模型，因此该项工作在基因组学、流行病学和计量经济学等大数据领域具有重要的应用价值。

Data with corruption is one of the most important bottlenecks that impede the statistical inference in high dimensional cases, since the standard regularized methods such as Lasso will generate unstable, biased or even misleading results now. This project aims at to provide some unified correction approaches for the high dimensional varying coefficient partially linear model, in which the parametric covariate is carried with two types of contamination including measurement error or missing at random, along with the related theoretical analysis. Firstly, we integrate the two corrupted model structures into the same one model framework with additive errors, and then transform the new model into a high dimensional linear model for studying through orthogonality-projection procedure. Secondly, for the normal and non-normal model errors, we do some sparse inference based on the obtained parametric model via bias-corrected weighted least squares Lasso and weighted quantile Lasso methods, respectively. During the process, we will employ different skills including convex conditional Lasso and conic programming, to deal with the related non-convex regularized objective functions. Thirdly, we establish the consistency of model selection for the new methods under some regularity assumptions on sparsity, and then present the upper bounds of the estimate error in terms of different norms. Our proposed methods are suitable for high/ultra-high dimensional sparse model, so this work has great applications in the areas of big data like genomics, epidemiology and econometrics, for instance.