Glossary of economics research
Results of search for GLS follow:
GLS:
Generalized Least Squares. A generalization of the OLS procedure to make an
efficient linear regression estimate of a parameter from a sample in which the
disturbances are heteroskedastic. That is, in
y = Xb + e (equation 1)
that the e's vary in magnitude with the X's.
The estimator of b is: (X'O-1X)-1X'O-1y
(equation 2)
where O, standing for omega, is the covariance matrix. (As you see in the
estimator, the covariance matrix is assumed to be invertible.)
The procedure to derive this is to multiply through the first equation by the
square root of the inverse of the covariance matrix (which assumed to be
known; if it estimated, one calls this procedure FGLS, for feasible GLS.)
Then take OLS of the resulting equation.
Contexts: econometrics
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