超高维线性回归模型的一种方差估计  

An Estimator of Variance in Ultrahigh Dimensional Linear Regression

作　　者：李济洪 闫文楠 王钰 杨杏丽[2] 

机构地区：[1]山西大学软件学院,山西太原030006 [2]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2017年第4期725-731,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家社会科学基金(16BTJ034)

摘　　要：超高维线性回归中的方差估计问题是超高维回归分析中需要解决的关键问题。针对在超高维线性回归中普通最小二乘法得到的方差估计存在有偏性的问题,有学者基于标准二折交叉验证提出了一种新的方差估计方法RCV。但发现方差的RCV估计依赖于数据的切分,稳定性差。为此,文章提出用组块3×2交叉验证的方法进行方差估计,并通过模拟实验将其与RCV方法进行了比较,验证了组块3×2交叉验证估计比RCV估计更为稳定。Variance estimation in ultrahigh dimensional linear regression is a key problem of regression analysis. In view of the biasedness of variance estimator based on ordinary least square, a new variance estimator based on a standard 2-fold cross-validation is proposed, denoted as RCV （refitted cross validation）. However, the RCV estimator of variance （severely） relies on the data partitioning, and it easily results in poor stability. Thus, a variance estimator based on blocked 3 ×2 cross-validation is proposed. The simulated comparisons further demonstrate that the variance estimator based on blocked 3 ×2 cross-validation is more stable than that of RCV.

关 键 词：超高维回归 数据切分 组块3×2交叉验证 方差估计 

分 类 号：O212[理学—概率论与数理统计]