Abstract
The efficiency of the ordinary least squares estimator (OLSE) b of β in the linear regression model y=Xβ+u, where E[u]=0, E[uu']=Σ is considered. The efficiency (EFF) of OLSE is defined by EFF=|var[β]|/|var[b]|, where β is the generalized least squares estimator (GLSE) of β.
Considering 1/EFF instead of EFF, the mean efficiency E[1/EFF] is obtained when the design matrix X is taken arbitrarily, i.e., X has the uniform distribution on the Stiefel manifold. Examples are given to compare E[1/EFF] with the upper bound of 1/EFF.
