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

Banerjee, A.N.; Magnus, J.R.

Abstract

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

Citation

Banerjee, A., & Magnus, J. (2000). On the sensitivity of the usual t- and F-tests to covariance misspecification. Journal of Econometrics, 95(1), 157-176. https://doi.org/10.1016/s0304-4076%2899%2900034-2

• Journal Article Type: Article
• Publication Date: 2000-03
• Deposit Date: Nov 24, 2014
• Journal: Journal of Econometrics
• Print ISSN: 0304-4076
• Electronic ISSN: 1872-6895
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Issue: 1
• Pages: 157-176
• DOI: https://doi.org/10.1016/s0304-4076%2899%2900034-2
• Keywords: Linear regression, Least squares, t-test, F-test, Autocorrelation, Sensitivity, Robustness.
• Public URL: https://durham-repository.worktribe.com/output/1417221