Factor profiled sure independence screening

• 成果类型: Article
• 署名作者: Wang, H.
• 署名单位: Peking University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asr074
• 发表日期: 2012
• 页码: 1528
• 关键词: nonconcave penalized likelihood; diverging number; model selection; variable selection; adaptive lasso; regression; dimension; shrinkage

摘要

We propose a method of factor profiled sure independence screening for ultrahigh-dimensional variable selection. The objective of this method is to identify nonzero components consistently from a sparse coefficient vector. The new method assumes that the correlation structure of the high-dimensional data can be well represented by a set of low-dimensional latent factors, which can be estimated consistently by eigenvalue-eigenvector decomposition. The estimated latent factors should then be profiled out from both the response and the predictors. Such an operation, referred to as factor profiling, produces uncorrelated predictors. Therefore, sure independence screening can be applied subsequently and the resulting screening result is consistent for model selection, a major advantage that standard sure independence screening does not share. We refer to the new method as factor profiled sure independence screening. Numerical studies confirm its outstanding performance.