Rank-based variable selection

This note considers variable selection in the robust linear model via R-estimates. The proposed rank-based approach is a generalisation of the penalised least-squares estimators where we replace the least-squares loss function with Jaeckel's (1972) dispersion function. Our rank-based method is robust to outliers in the errors and has roots in traditional non-parametric statistics for simple location-shift problems. We establish the theoretical properties of our estimators which ensure desirable asymptotic behaviour of setting coefficient estimates to zero for unimportant variables and consistently estimating coefficients for important variables. Numerical studies indicate that the rank-based methods perform well for both light- and heavy-tailed error distributions.