Generalized least squares

Summary

Generalized least squares estimates the coefficients of a linear model whose errors have a known covariance structure that is not a multiple of the identity. It minimises a squared distance weighted by the inverse of the error covariance matrix. Under the analogue of the Gauss–Markov theorem, due to Aitken, it is the best linear unbiased estimator in that setting. Weighted least squares is the special case of uncorrelated errors with unequal variances.