[R] GLS terminology question not related to R
p.dalgaard at biostat.ku.dk
Wed Apr 25 21:13:22 CEST 2007
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.
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