一种改进的Lasso方法及其在对数线性模型中的应用  

An improved Lasso method and its application in log-linear models

作　　者：李春红[1] 黄登香 覃朝勇[1] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《广西大学学报（自然科学版）》2015年第3期758-765,共8页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11361007);广西自然科学基金资助项目(2012GXNSFBA053010);广西自然科学基金资助项目(2011GXNSFA018126)

摘　　要：变量选择在数据分析中有着重要应用,其参数估计的渐近性质,特别是Oracle性质及组效应性质在变量选择方法上尤其重要。针对Lasso方法一般情形下不具有Oracle性质及组效应性质,将探讨Lasso的一种改进方法,即Adaptive elastic net方法在Poisson对数线性模型的应用,证明当满足一定条件时,Adaptive elastic net方法估计具有Oracle性质及组效应性质,并利用数值模拟验证其优良性。Variable selection plays an important role in data analysis. Its asymptotic properties of parametric estimation （ especially the Oracle properties and the group effect） are particularly impor-tant. However, the Lasso method does not have the two properties in general. To remedy this draw-back, in this paper an improved Lasso method is proposed, which applies the Adaptive Elastic Net method to the Poisson log-linear models. It is proved that the Adaptive Elastic Net procedure estima-tor has the Oracle properties and the group effect under some appropriate conditions. The numerical simulation also confirms the superiority of the proposed method.

关 键 词：ADAPTIVE ELASTIC net方法 Poisson对数线性模型 Oracle性质 组效应 

分 类 号：O212.1[理学—概率论与数理统计]