ON THE ADAPTIVE ELASTIC-NET WITH A DIVERGING NUMBER OF PARAMETERS

• 成果类型: Article
• 署名作者: Zou, Hui; Zhang, Hao Helen
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; North Carolina State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS625
• 发表日期: 2009
• 页码: 1733-1751
• 关键词: nonconcave penalized likelihood; variable selection; shrinkage; Lasso; MODEL

摘要

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 [J Amer. Statist. Assoc. 96 (2001) 1348-1360] and [Ann. Statist. 32 (2004) 928-961] 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.