Forward Regression for Ultra-High Dimensional Variable Screening

• 成果类型: Article
• 署名作者: Wang, Hansheng
• 署名单位: Peking University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2008.tm08516
• 发表日期: 2009
• 页码: 1512-1524
• 关键词: nonconcave penalized likelihood; diverging number; model selection; adaptive lasso; bridge

摘要

Motivated by the seminal theory of Sure Independence Screening (Fan and Lv 2008, SIS), we investigate here another popular and classical variable screening method, namely, forward regression (FR). Our theoretical analysis reveals that FR can identify all relevant predictors consistently, even if the predictor dimension is substantially larger than the sample size. In particular, if the dimension of the true model is finite, FR can discover all relevant predictors within a finite number of steps. To practically select the best candidate from the models generated by FR, the recently proposed BIC criterion of Chen and Chen (2008) can be used. The resulting model can then serve as an excellent starting point, from where many existing variable selection methods (e.g., SCAD and Adaptive LASSO) can be applied directly. FR's outstanding finite sample performances are confirmed by extensive numerical studies.