基于SCAD_L_(2)和SCAD混合惩罚的高维随机效应线性回归模型

High Dimensional Random Effects Linear Regression Model Based on Mixed Penalties of SCAD_L_(2) and SCAD

大数据时代的到来,使得变量选择问题成为了当前统计界和各重要领域实际工作者研究的重点课题在许多实际问题中,由于数据间存在相关性或异方差,对高维模型进行变量选择时会产生较大的系统性偏差。该文考虑高维随机效应线性回归模型,改进了现有的基于双惩罚思想的变量选择方法,提出了基于SCAD_L_(2)和SCAD的混合惩罚方法,在一定程度上弥补了已有方法不同时具备分组效应和渐近性质的不足:给出了基于混合惩罚的随机效应线性回归模型的两步迭代算法.分别在信噪比和随机效应影响不同的情况下对模型进行蒙特卡洛模拟和实例验证.结果表明:与其他惩罚方法相比,该混合惩罚方法具有分组效应和渐近性质,表现出更优良的变量选择能力和系数估计效果,适用于高维随机效应线性回归模型.

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 prac-tical 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 abil-ity and coefficient estimation effect,and is suitable for high-dimensional random effect linear regression models.