Hostname: page-component-6bf8c574d5-r8w4l Total loading time: 0 Render date: 2025-03-04T04:26:31.689Z Has data issue: false hasContentIssue false
  • English
  • Français

A Variance Comparison of OLS and Feasible GLS Estimators

Published online by Cambridge University Press:  18 October 2010

David Grubb  and
Lonnie Magee
David Grubb
Affiliation:
OECD Directorate for Social Affairs
Lonnie Magee
Affiliation:
McMaster University
Get access Rights & Permissions [Opens in a new window]

Abstract

Second-order approximations to the variances of OLS and GLS estimators are compared when the covariance matrix is locally nonscalar. Using a result of Rothenberg, the comparison of OLS and GLS variances is shown to be asymptotically equivalent to a weighted mean square error comparison of the error covariance parameter estimators used in those two procedures. When there is only one covariance parameter, this comparison depends only on the noncentrality parameter of a classical hypothesis test for a scalar covariance matrix.

Type
Brief Report
Information
Econometric Theory , Volume 4 , Issue 2 , August 1988 , pp. 329 - 335
Copyright
Copyright © Cambridge University Press 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Engle, R. Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflations. Econometrica 50 (1982): 987–1007.10.2307/1912773Google Scholar
2. Godfrey, L.G. On the invariance of the Lagrange multiplier test with respect to certain changes in the alternative hypothesis. Econometrica 49 (1981): 1443–1456.10.2307/1911410Google Scholar
3. Gourieroux, C. & Trognon, A.. Specification pretest estimator. Journal of Econometrics 25 (1984): 15–27.10.1016/0304-4076(84)90033-2Google Scholar
4. Hong, D.M. & L'Esperance, W.L.. Effects of autocorrelated errors on various least squares estimators: a Monte Carlo study. Communications in Statistics 2 (1973): 507–523.10.1080/03610927308827094Google Scholar
5. Rao, P. & Griliches, Z.. Small-sample properties of several two-stage regression methods in the context of autocorrelated disturbances. Journal of the American Statistical Association 64 (1969): 253–272.10.1080/01621459.1969.10500968Google Scholar
6. Rothenberg, T.J. Approximate normality of generalized least squares estimates. Econometrica 52 (1984): 811–825.10.2307/1911185Google Scholar
7. Ruud, P. Tests of specification in econometrics. Econometric Reviews 3 (1984): 211–242.10.1080/07474938408800065Google Scholar
8. Sen, P.K. Asymptotic properties of maximum likelihood estimators based on conditional specification. Annals of Statistics 7 (1979): 1019–1033.10.1214/aos/1176344785Google Scholar
9. Spitzer, J.J. Small-sample properties of nonlinear least squares and maximum likelihood estimators in the context of autocorrelated errors. Journal of the American Statistical Association 74 (1979): 41–47.10.1080/01621459.1979.10481605Google Scholar
10. Toro-Vizcarrondo, G. & Wallace, T.D.. Test of the mean square error criterion for restrictions in linear regressions. Journal of the American Statistical Association 63 (1968): 558–572.Google Scholar