Banerjee, Anurag N. and Magnus, Jan R.
The sensitivity of OLS when variance matrix is (partially) unknown
Journal of Econometrics, 92, (2), . (doi:10.1016/S0304-4076(98)00093-1).
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We consider the standard linear regression model y=X?+u with all standard assumptions, except that the variance matrix is assumed to be ?2?(?), where ? depends on m unknown parameters ?1,…, ?m. Our interest lies exclusively in the mean parameters ? or X?. We introduce a new sensitivity statistic (B1) which is designed to decide whether y (or B) is sensitive to covariance misspecification. We show that the Durbin–Watson test is inappropriate in this context, because it measures the sensitivity of Image to covariance misspecification. Our results demonstrate that the estimator Image and the predictor Image are not very sensitive to covariance misspecification. The statistic is easy to use and performs well even in cases where it is not strictly applicable.
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