在现代诸多复杂数据的统计推断或机器学习过程中，一个必要的环节就是所谓的“数据清洗”，而异常点探查是数据清洗的核心内容之一。只有找到这些异常点，后续数据分析结果的正确性和有效性才有保证。如果把n个p维样本看作n×p矩阵，最近已有一些工作研究在高维情形下此矩阵中行数据是否为异常，但在许多实际问题中，仅有某些观测值的个别分量出现异常的情况更为普遍。而本项目则将侧重研究如何通过充分利用变量相关性，有效地探查矩阵中的元素异常点，开发稳健的识别方案。我们将首先针对一般的大规模数据矩阵开展研究，之后拓展至对线性模型和广义线性模型中的协变量观测矩阵中的异常值的研究，最后研究函数型数据中的异常点探查与检验。由于数据是高维的，故为了更好地控制错误识别率，我们将深入研究如何利用knock-off方法来控制筛选的FDR，并详尽研究崩溃点性质和筛选的相合性问题。

In the modern statistical inference or machine learning process of complex data, a necessary step is the so-called "data cleaning", and outlier detection is one of the key procedures of data cleaning. Only when these outlying points are found, the correctness and validity of the subsequent data analysis results could be guaranteed. Consider a multivariate dataset consists of n cases in p dimensions, and is often stored in an n by p data matrix. It is well-known that real data may contain outliers. In statistics and data analysis the word outlier usually refers to a row of the data matrix, and the methods to detect such outliers only work when at least half the rows are clean. But often many rows have a few contaminated cell values, which may not be visible by looking at each variable (column) separately. In this project, we aim to design new methods to detect deviating data cells in a high-dimensional sample which takes the correlations between the variables into account. .We will focus on the standard large matrix data, and extend the approaches to the linear model or generalized linear model, as well the functional data. The proposed method can serves as an initial step for massive data analysis. To better control the error rate, we will delve into how to use the knock-off method to control the FDR, and thoroughly study the breakdown point and the identification consistency of the proposed method.