Smoothly clipped absolute deviation on high dimensions

Yongdai Kim, Hosik Choi, Hee Seok Oh

Research output: Contribution to journalArticlepeer-review

192 Scopus citations

Abstract

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 an 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.

Original languageEnglish
Pages (from-to)1665-1673
Number of pages9
JournalJournal of the American Statistical Association
Volume103
Issue number484
DOIs
StatePublished - Dec 2008

Keywords

  • High dimension
  • Oracle property
  • Regression
  • Regularization
  • Smoothly clipped absoluetly deviation penalty

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