Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
Hostname: page-component-5c569c448b-4wdfl Total loading time: 0.228 Render date: 2022-07-02T21:37:06.066Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true
  • English
Econometric Theory Econometric Theory

Article contents

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

1. Engle, R. Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflations. Econometrica 50 (1982): 987–1007.10.2307/1912773CrossRefGoogle 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): 1443–1456.10.2307/1911410CrossRefGoogle Scholar
3. Gourieroux, C. & Trognon, A.. Specification pretest estimator. Journal of Econometrics 25 (1984): 15–27.10.1016/0304-4076(84)90033-2CrossRefGoogle 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): 507–523.10.1080/03610927308827094CrossRefGoogle 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): 253–272.10.1080/01621459.1969.10500968CrossRefGoogle Scholar
6. Rothenberg, T.J. Approximate normality of generalized least squares estimates. Econometrica 52 (1984): 811–825.10.2307/1911185CrossRefGoogle Scholar
7. Ruud, P. Tests of specification in econometrics. Econometric Reviews 3 (1984): 211–242.10.1080/07474938408800065CrossRefGoogle 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/1176344785CrossRefGoogle 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): 41–47.10.1080/01621459.1979.10481605CrossRefGoogle 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
9
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A Variance Comparison of OLS and Feasible GLS Estimators
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

A Variance Comparison of OLS and Feasible GLS Estimators
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

A Variance Comparison of OLS and Feasible GLS Estimators
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *