The sensitivity of OLS when the variance matrix is (partially) unknown

摘要

We consider the standard linear regression model y = X#beta# + u with all standard assumptions, except that the variance matrix is assumed to be #sigma#~2#OMEGA#(#theta#), where #OMEGA# depends on m unknown parameters #theta#_1, ..., #theta#_m. Our interest lies exclusively in the mean parameters #beta# or X#beta#. We introduce a new sensitivity statistic (B1) which is designed to decide whether y (or #beta#) is sensitive to covariance misspecification. We show that the Durbin-Watson test is inappropriate in this context, because it measures the sensitivity of #sigma#~2 to covariance misspecification. Our results demonstrate that the estimator #beta# and the predictor y 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.