Rank-based group variable selection

Abstract

A robust rank-based estimator for variable selection in linear models, with grouped predictors, is studied. The proposed estimation procedure extends the existing rank-based variable selection [Johnson, B.A., and Peng, L. (2008), ‘Rank-based Variable Selection’, Journal of Nonparametric Statistics, 20(3):241–252] and the ww-scad [Wang, L., and Li, R. (2009), ‘Weighted Wilcoxon-type Smoothly Clipped Absolute Deviation Method’, Biometrics, 65(2):564–571] to linear regression models with grouped variables. The resulting estimator is robust to contamination or deviations in both the response and the design space.The Oracle property and asymptotic normality of the estimator are established under some regularity conditions. Simulation studies reveal that the proposed method performs better than the existing rank-based methods [Johnson, B.A., and Peng, L. (2008), ‘Rank-based Variable Selection’, Journal of Nonparametric Statistics, 20(3):241–252; Wang, L., and Li, R. (2009), ‘Weighted Wilcoxon-type Smoothly Clipped Absolute Deviation Method’, Biometrics, 65(2):564–571] for grouped variables models. This estimation procedure also outperforms the adaptive hlasso [Zhou, N., and Zhu, J. (2010), ‘Group Variable Selection Via a Hierarchical Lasso and its Oracle Property’, Interface, 3(4):557–574] in the presence of local contamination in the design space or for heavy-tailed error distribution.