On the bias of some least-squares estimators of variance in a general linear model

Watson (1955) investigated the performance of a regression analysis based on the assumption that the error covariance matrix is o2y when it is, in fact, o2x. In the present paper Watson's results regarding the effects of this type of specification error on the bias of estimators of variance are generalized. In particular, we give, for arbitrary design matrices of full rank, attainable bounds for the bias of the least-squares estimator of the variance of arbitrary linear functions of the estimated regression coefficients.