Shrinkage Estimator of SCAD and Adaptive Lasso penalties in Quantile Regression Model

Abstract

Quantile regression is one of the most frequently used topics in data analysis. In this article, we proposed the shrinkage estimator for penalized quantile regression that combines SCAD (Smoothly Clipped Absolute Deviation) and Adaptive Lasso estimators. these estimators were compared by using simulationstudies based on statistical measures, mean squared error (MSE), false positive rate (FPR) and false negative rate (FNR).After applying theSimulation studies it was found that the proposed estimator is the best in estimation and selection of variable because it has the lowest mean squared error (MSE) and   it has lowest False Positive Rate (FPR) and False Negative Rate (FNR).