Smoothly Clipped Absolute Deviation on High Dimensions

• 成果类型: Article
• 署名作者: Kim, Yongdai; Choi, Hosik; Oh, Hee-Seok
• 署名单位: Seoul National University (SNU); Hoseo University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214508000001066
• 发表日期: 2008
• 页码: 1665-1673
• 关键词: nonconcave penalized likelihood; variable selection; oracle properties; model selection; Lasso; regularization; persistence

摘要

The smoothly clipped absolute deviation (SCAD) estimator, proposed by Fan and Li, has many desirable properties, including continuity, sparsity, and unbiasedness. The SCAD estimator also has the (asymptotically) oracle property when the dimension of covariates is fixed or diverges more slowly than the sample size. In this article we study the SCAD estimator in high-dimensional settings where the dimension of covariates can be much larger than the sample size. First, we develop and efficient optimization algorithm that is fast and always converges to a local minimum. Second, we prove that the SCAD estimator still has the oracle property on high-dimensional problems. We perform numerical studies to compare the SCAD estimator with the LASSO and SIS-SCAD estimators in terms of prediction accuracy and variable selectivity when the true model is sparse. Through the simulation, we show that the variance estimator of Fan and Li still works well for some limited high-dimensional cases where the true nonzero coefficients are not too small and the sample size is moderately large. We apply the proposed algorithm to analyze a high-dimensional microarray data set.