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.
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This is not an offer (or solicitation of an offer) to buy/se...{{dropped}}
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
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. > >