Robust variable selection and estimation via adaptive elastic net S-estimators for linear regression

Heavy-tailed error distributions and predictors with anomalous values are ubiquitous in high-dimensional regression problems can seriously jeopardize the validity of statistical analyses if not properly addressed. For more reliable variable selection prediction under these adverse conditions, adaptive PENSE, a new robust regularized estimator, is proposed. Adaptive PENSE yields coefficient estimates even aberrant contamination or residuals. It shown that penalty leads to than other penalties, particularly presence gross outliers predictor space. further demonstrated has strong properties it possesses oracle property heavy-tailed errors without need estimate scale. Numerical studies on simulated real data sets highlight superior finite-sample performance vast range settings compared estimators case contaminated samples. An R package implementing fast algorithm for computing proposed method additional simulation results provided supplementary materials.