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

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.