On the Efficiencies of Several Generalized Least Squares Estimators in a Seemingly Unrelated Regression Model and a Heteroscedastic Model

This paper investigates the efficiencies of several generalized least squares estimators (GLSEs) in terms of the covariance matrix. Two models are analyzed: a seemingly unrelated regression model and a heteroscedastic model. In both models, we define a class of unbiased GLSEs and show that their covariance matrices remain the same even if the distribution of the error term deviates from the normal distributions. The results are applied to the problem of evaluating the lower and upper bounds for the covariance matrices of the GLSEs.