Robust Variable Selection and Regularization in Quantile Regression Based on Adaptive-LASSO and Adaptive E-NET

Although the variable selection and regularization procedures have been extensively considered in literature for quantile regression (QR) scenario via penalization, many such fail to deal with data aberrations design space, namely, high leverage points (X-space outliers) collinearity challenges simultaneously. Some referred as influential observations tend adversely alter eigenstructure of matrix by inducing or masking collinearity. Therefore, literature, it is recommended that problems should be dealt In this article, we suggest adaptive LASSO E-NET penalized QR (QR-ALASSO QR-AE-NET) where weights are based on a estimator remedies. We extend methodology their weighted versions WQR-LASSO, WQR-E-NET had suggested earlier. RIDGE (RR) parameter estimator. use may plausible at ℓ1 (QR τ=0.5) symmetrical distribution, not so extreme levels. QR-based derive weights. carried out comparative study QR-LASSO, QR-E-NET, ones here, viz., QR-ALASSO, QR-AE-NET, QRALASSO AE-NET (WQR-ALASSO WQR-AE-NET) procedures. The simulation results show WQR-ALASSO WQR-AE-NET generally outperform nonadaptive counterparts. At predictor matrices under normality, QR-ALASSO respectively, non-adaptive unweighted scenarios, follows: all 16 cases (100%) respect correctly selected (shrunk) zero coefficients; 88% fitted models; 81% prediction. WQR 75% time both models shrunk coefficients 63% scenarios prediction, 100% time; 50% (while equally); time. scenario, respective follows; models, while t-distribution, QR-AE-NET each; Additionally, result former outperforming latter prediction whilst there no clear "winner" other two measures. Overall, outperforms collinearity-masking outperformed metrics. dominate 38% 62% coefficients. vice-versa cases. heavy-tailed distributions (t-distributions d∈(1;6) degrees freedom) dominance over again evident. they perform better time, coefficients, cases; do Results from applications real life sets more less line studies results.