Weighted wilcoxon-type smoothly clipped absolute deviation method

Lan Wang, Runze Li

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

Shrinkage-type variable selection procedures have recently seen increasing applications in biomedical research. However, their performance can be adversely influenced by outliers in either the response or the covariate space. This article proposes a weighted Wilcoxon-type smoothly clipped absolute deviation (WW-SCAD) method, which deals with robust variable selection and robust estimation simultaneously. The new procedure can be conveniently implemented with the statistical software R. We establish that the WW-SCAD correctly identifies the set of zero coefficients with probability approaching one and estimates the nonzero coefficients with the rate n-1/2. Moreover, with appropriately chosen weights the WW-SCAD is robust with respect to outliers in both the x and y directions. The important special case with constant weights yields an oracle-type estimator with high efficiency in the presence of heavier-tailed random errors. The robustness of the WW-SCAD is partly justified by its asymptotic performance under local shrinking contamination. We propose a Bayesian information criterion type tuning parameter selector for the WW-SCAD. The performance of the WW-SCAD is demonstrated via simulations and by an application to a study that investigates the effects of personal characteristics and dietary factors on plasma beta-carotene level.

Original languageEnglish (US)
Pages (from-to)564-571
Number of pages8
JournalBiometrics
Volume65
Issue number2
DOIs
StatePublished - Jun 2009

Keywords

  • Leverage points
  • Oracle property
  • Outlier
  • Rank-based analysis
  • Robust estimation
  • Robust model selection
  • Shrinking contamination
  • Smoothly clipped absolute deviation
  • Wilcoxon method

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