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On the sensitivity of the usual t- and F-tests to covariance misspecification

On the sensitivity of the usual t- and F-tests to covariance misspecification
On the sensitivity of the usual t- and F-tests to covariance misspecification
We consider the standard linear regression model with all standard assumptions, except that the disturbances are not white noise, but distributed N(0, ?2?(?)) where ?(0)=In. Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are not interested in finding out whether ?=0 or not. Instead we want to find out what the effect is of possibly nonzero ? on the F-statistic itself. We propose a sensitivity statistic small phi, Greek for this purpose, discuss its distribution, and obtain a practical and easy-to-use decision rule to decide whether the F-test is sensitive or not to covariance misspecification when ? is close to zero. Some finite and asymptotic properties of curly or open small phi, Greek are studied, as well as its behaviour in the special case of an AR(1) process near the unit root
linear regression, least squares, t-test, F-test, autocorrelation, sensitivity, robustness
0304-4076
157-176
Banerjee, Anurag N.
4f772e58-24c0-4266-ba41-18f70a6108c4
Magnus, Jan R.
0aca9de5-9fa8-4d0b-9b02-8fe657aa3d92
Banerjee, Anurag N.
4f772e58-24c0-4266-ba41-18f70a6108c4
Magnus, Jan R.
0aca9de5-9fa8-4d0b-9b02-8fe657aa3d92

Banerjee, Anurag N. and Magnus, Jan R. (2000) On the sensitivity of the usual t- and F-tests to covariance misspecification. Journal of Econometrics, 95 (1), 157-176. (doi:10.1016/S0304-4076(99)00034-2).

Record type: Article

Abstract

We consider the standard linear regression model with all standard assumptions, except that the disturbances are not white noise, but distributed N(0, ?2?(?)) where ?(0)=In. Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are not interested in finding out whether ?=0 or not. Instead we want to find out what the effect is of possibly nonzero ? on the F-statistic itself. We propose a sensitivity statistic small phi, Greek for this purpose, discuss its distribution, and obtain a practical and easy-to-use decision rule to decide whether the F-test is sensitive or not to covariance misspecification when ? is close to zero. Some finite and asymptotic properties of curly or open small phi, Greek are studied, as well as its behaviour in the special case of an AR(1) process near the unit root

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More information

Published date: 2000
Additional Information: JEL classification codes: C12, C22, C51, C52
Keywords: linear regression, least squares, t-test, F-test, autocorrelation, sensitivity, robustness

Identifiers

Local EPrints ID: 32930
URI: https://eprints.soton.ac.uk/id/eprint/32930
ISSN: 0304-4076
PURE UUID: 67b1607e-3aaf-41cd-a2e6-faae5ffc0382

Catalogue record

Date deposited: 18 Jul 2006
Last modified: 17 Jul 2017 15:54

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