Improved LASSO

TL;DR

This paper introduces an improved LASSO estimation method based on Stein-rule principles, which enhances variable selection and estimation accuracy in regression models through shrinkage techniques.

Contribution

It develops a novel Stein-type LASSO estimator incorporating preliminary test and positive-rule shrinkage, demonstrating improved performance over traditional methods.

Findings

Stein-type LASSO outperforms classical LASSO in risk ordering.

Simulation results confirm the effectiveness across various correlation and parameter configurations.

Real data examples validate practical usefulness of the proposed estimators.

Abstract

We propose an improved LASSO estimation technique based on Stein-rule. We shrink classical LASSO estimator using preliminary test, shrinkage, and positive-rule shrinkage principle. Simulation results have been carried out for various configurations of correlation coefficients ($r$), size of the parameter vector ($\beta$), error variance ($\sigma^2$) and number of non-zero coefficients ($k$) in the model parameter vector. Several real data examples have been used to demonstrate the practical usefulness of the proposed estimators. Our study shows that the risk ordering given by LSE $>$ LASSO $>$ Stein-type LASSO $>$ Stein-type positive rule LASSO, remains the same uniformly in the divergence parameter $\Delta^2$ as in the traditional case.