Penalized least squares
= Penalized least squares
= Penalised least squares
{synonym}
For $\lambda\geq0$, a full-column-rank <design matrix> $B$, and a <positive semidefinite matrix> $\Omega$, minimize $\|y-B\beta\|^2+\lambda\beta^T\Omega\beta$. Differentiation gives $(B^TB+\lambda\Omega)\widehat\beta=B^Ty$. The fitted-value matrix is $B(B^TB+\lambda\Omega)^{-1}B^T$, whose trace measures the <effective degrees of freedom>.