A New Quantile-Based Approach for LASSO Estimation

Abstract

Regularization regression techniques are widely used to overcome a model’s parameter estimation problem in the presence of multicollinearity. Several biased techniques are available in the literature, including ridge, Least Angle Shrinkage Selection Operator (LASSO), and elastic net. In this work, we study the performance of the classical LASSO, adaptive LASSO, and ordinary least squares (OLS) methods in high-multicollinearity scenarios and propose some new estimators for estimating the LASSO parameter “k”. The performance of the proposed estimators is evaluated using extensive Monte Carlo simulations and real-life examples. Based on the mean square error criterion, the results suggest that the proposed estimators outperformed the existing estimators.

Keywords

• LASSO
• regularization methods
• multicollinearity
• high-dimensional data
• Monte Carlo