A robust and efficient change point detection method for high-dimensional linear models

In the context of linear models, a key problem of interest is to estimate the regression coefficient. Nevertheless, in certain instances, the vector of unknown coefficient parameters in a linear regression model differs from one segment to another. In this paper, when the dimension of covariates is high, a new method is proposed to examine a linear model in which the regression coefficient of two subpopulations may be different. To achieve robustness and efficiency, we introduce modal linear regression as a means of estimating the unknown coefficient parameters. Furthermore, our proposed method is capable of selecting variables and checking change points. Under certain mild assumptions, the limiting behavior of our proposed method can be established. Additionally, an estimation algorithm based on kick-one-off and SCAD approach is developed to implement in practice. For illustration, simulation studies and a real data are considered to assess the performance of our proposed method.