Tuning relation between Lasso and square-root Lasso
= Tuning relation between Lasso and square-root Lasso
{title2=$\gamma=\lambda/\widehat\sigma_\lambda$}
A <Lasso> minimizer with positive residual scale $\widehat\sigma_\lambda=\|Y-X\widehat\beta_\lambda\|_2/\sqrt n$ also minimizes the <Square-root Lasso> objective at the displayed tuning parameter. Divide its <Karush-Kuhn-Tucker conditions> by the residual scale and use the <subgradient optimality condition>.