Shrinkage-type variable selection procedures have recently seen increasing appli cations in biomedical research.However, their performance can be adversely influ enced by outliers in either the response or the covariate space.This paper 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 root n rate.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 at the pres ence 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 BIC-typc 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.