Weighted least squares

Weighted least squares minimizes ${\sum }_i{w}_i(Y_i-X_i^T\beta {)}^2$; inverse-variance weights give the efficient estimator under known heteroscedasticity.

Generalized least squares minimizes $(Y-X\beta {)}^T{\Omega }^{-1}(Y-X\beta )$ for a known covariance shape $\Omega$.

Whitening multiplies a model by a square root of its precision matrix so that the transformed errors have identity covariance.