Unified LASSO estimation by least squares approximation

• 成果类型: Article
• 署名作者: Wang, Hansheng; Leng, Chenlei
• 署名单位: Peking University; National University of Singapore
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214507000000509
• 发表日期: 2007
• 页码: 1039-1048
• 关键词: VARIABLE SELECTION; oracle properties; model selection; censored-data; regression; CLASSIFICATION; asymptotics; shrinkage

摘要

We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Specifically, LSA can transfer many different types of LASSO objective functions into their asymptotically equivalent least squares problems. Thereafter, the standard asymptotic theory can be established and the LARS algorithm can be applied. In particular, if the adaptive LASSO penalty and a Bayes information criterion-type tuning parameter selector are used, the resulting LSA estimator can be as efficient as the oracle. Extensive numerical studies confirm our theory.