Improved LASSO
This provides incremental improvements to LASSO estimation for statistical modeling applications.
The authors tackled the problem of improving LASSO estimation by proposing Stein-rule based techniques that incorporate preliminary test, shrinkage, and positive-rule shrinkage principles. Their results show a consistent risk ordering where their Stein-type positive rule LASSO performs best, with simulations and real data demonstrating practical usefulness.
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 ($β$), error variance ($σ^2$) 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 $Δ^2$ as in the traditional case.