Overview of Robust Variable Selection Methods for High-Dimensional Linear Regression Model

With the advance of the era of big data, high-dimensional data are frequently collected in many research fields such as economics, finance, and biomedicine. One of the characteristics of high-dimensional data is that the variable dimension p increases with the increase of the sample size n and usually exceeds the sample size. At the same time, outliers are also prone to appear in high-dimensional data. Therefore, how to overcome the influence of outliers on high-dimensional statistical inference, so as to obtain a more accurate model, is one of the hot issues in current statistical research. This paper is an overview of robust variable selection methods under high-dimensional linear models. Specifically, first of all, we introduce three indicators to evaluate robustness: influence function, breakdown point and maximum deviation. Secondly, it focuses on the selection methods of robust variables, including response variables with outliers, response variables and covariates with outliers, high breakdown point and efficient variable selection methods. Then, the related algorithms are introduced, and different variable selection methods are compared through simulation and examples. Finally, the problems of high-dimensional robust effective variable selection methods and the possible development direction in the future are briefly discussed.