Lasso reduction for the Lava estimator
= Lasso reduction for the Lava estimator
For $Q=(X^TX+2n\lambda_2I)^{-1}$ and $A=(I-XQX^T)^{1/2}$, profiling the dense coefficient gives $\widehat\beta=QX^T(Y-X\widehat\delta)$. The sparse coefficient minimizes $\|AY-AX\delta\|_2^2/(2n)+\lambda_1\|\delta\|_1$. The transformation uses the <principal square root of a positive semidefinite matrix> and remains valid for rank-deficient designs.