A Note on Estimation Error Bound and Grouping Effect of Transfer Elastic Net

The Transfer Elastic Net is an estimation method for linear regression models that combines ${\mathrm{\ell }}_1$ and ${\mathrm{\ell }}_2$ norm penalties to facilitate knowledge transfer. In this study, we derive a non-asymptotic ${\mathrm{\ell }}_2$ norm estimation error bound for the estimator and discuss scenarios where the Transfer Elastic Net effectively works. Furthermore, we examine situations where it exhibits the grouping effect, which states that the estimates corresponding to highly correlated predictors have a small difference.