In a general normal regression model, this paper first derives the least upper bound (LUB) for the covariance matrix of a generalized least squares estimator (GLSE) relative to the covariance matrix of the Gauss-Markov estimator. Second the result is applied to the (unrestricted) Zellner estimator in an N-equation seemingly unrelated regression (SUR) model and to the GLSE in a heteroscedastic model.
"Least upper bound for the covariance matrix of a generalized least squares estimator in regression with applications to a seemingly unrelated regression model and a heteroscedastic model." Ann. Statist. 24 (4) 1547 - 1559, August 1996. https://doi.org/10.1214/aos/1032298283