缺失数据下超高维线性模型的变量筛选

Variables screening of ultra-high dimensional linear model with missing data

在响应变量随机缺失情形下,研究超高维线性模型的确定性独立变量筛选问题.首先,使用逻辑线性回归模型拟合响应变量的缺失变量与相应协变量,估计响应变量的缺失概率;然后,建立基于逆概率加权最小二乘的效用函数,通过它将协变量维数降到较低水平;最后,运用基于LASSO惩罚的逆概率加权最小二乘方法对协变量进行更精细的筛选,达到协变量超高维降维的目的.数值模拟和实例分析表明,所研究的变量筛选方法对有限样本的情形表现良好.

In the case of random missed response variables,the independent variable screening method for ultra-high dimensional linear model is considered.Firstly,the missing probability of response variables is estimated by using Logistic regression model for missing indicators and the corresponding covariates.Then,the inverse probability weighted quadratic loss utility functions are established to reduce the dimensionality to a low level.At last,a more refined variable selection method with LASSO penalty is used to the dimensional reduced data.Through some numerical simulation and a real data example,it is concluded that variable screening method is very satisfactory for moderate sample size.