Abstract:

With the advent of the era of big data, variable selection has become a key topic in the current statistical field and practical workers in various important fields. In many practical problems, due to the existence of correlation or heteroscedasticity between data, variable selection of high-dimensional models produce large systematic bias and low efficiency. In this paper, we consider high-dimensional random effect linear regression model, improve the existing variable selection method based on the idea of double penalty, and propose a hybrid penalty method based on SCAD_L$_2$ and SCAD, which makes up for the lack of both grouping effect and asymptotic property of the existing methods to a certain extent. A two-step iterative algorithm for random effect linear regression model based on mixed penalty is presented. Monte Carlo simulation and example verification are carried out under different SNR and random effects. Compared with other penalty methods, the results show that the hybrid penalty method not only has grouping effect and asymptotic property, but also shows better variable selection ability and coefficient estimation effect, and is suitable for high-dimensional random effect linear regression models.

Key words: SCAD_L $_2$ and SCAD mixed penalty method, High dimensional random effects linear regression model, Grouping effect, Asymptotic property