ON THE ADAPTIVE ELASTIC-NET WITH A DIVERGING NUMBER OF PARAMETERS.
We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property (Fan and Li, 2001; Fan and Peng, 2004) which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem which should be properly handled by the ideal method. Many existing variable selection methods fail to achieve both goals simultaneously. In this paper, we propose the adaptive Elastic-Net that combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage. Under weak regularity conditions, we establish the oracle property of the adaptive Elastic-Net. We show by simulations that the adaptive Elastic-Net deals with the collinearity problem better than the other oracle-like methods, thus enjoying much improved finite sample performance.
Zou
Hui
H
School of Statistics, University of Minnesota, Minneapolis, Mn 55455, E-Mail: hzou@stat.umn.edu.
Zhang
Hao Helen
HH
Ann Stat. 2008 Oct;36(5):2232-2260
19173010
Biometrika. 2007 Aug 1;94(3):553-568
19343105