[R] GLS terminology question not related to R

[Peter Dalgaard]

Thomas Lumley wrote:
> 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.
>   
Yes, and to complicate things further that is not necessarily true if 
many parameters go into determining the variances and covariances 
necessary for GLS. (Cue recent discussion comparing T^2 and F tests).
> 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.
>
>