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October 2021

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

Author(s): Magnus, J. R.

Journal/Book: J Econometrics. 2000; 95: PO Box 564, 1001 Lausanne, Switzerland. Elsevier Science Sa. 157-176.

Abstract: We consider the standard linear regression model with all standard assumptions, except that the disturbances are not white noise, but distributed N(0,sigma(2)Ohm(theta)) where Ohm(0) = I-n. Our interest lies in testing linear restrictions using the usual F-statistic based on OLS residuals. We are not interested in finding out whether theta = 0 or not. Instead we want to find out what the effect is of possibly nonzero theta on the F-statistic itself. We propose a sensitivity statistic phi 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 theta is close to zero. Some finite and asymptotic properties of phi are studied, as well as its behaviour in the special case of an AR(1) process near the unit root.

Note: Article Magnus JR, Tilburg Univ, CentER, POB 90153, NL-5000 LE Tilburg, NETHERLANDS

Keyword(s): linear regression; least squares; t-test; F-test; autocorrelation; sensitivity; robustness; AUTO-CORRELATION; REGRESSIONS; MODEL; POWER

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