[R] GLS terminology question not related to R

[Thomas Lumley]

On Wed, 25 Apr 2007, Leeds, Mark (IED) wrote:

> This is a terminology question not related to R. The literature often
> says that OLS is inefficient relative to GLS if the residuals in
> the system are correlated ( and the RHS sides of each are not identical
> ). Does this mean that OLS overestimates residual and coefficient
> variances , underestimates them or just gets them wrong and the
> direction is not known ? Thanks.

It does not mean either.

It means that the true variance of the OLS estimates is greater than the 
true variance of the GLS estimates.

A separate issue is whether the estimated variance of an OLS estimator is 
greater or less than the true variance of the OLS estimator.  This can go 
either way.

 	-thomas