@bullet @bullet a Note on the Effect of Estimating Weights in Weighted Least Squares

• ABSTRACT We consider heteroscedastic linear models for which the variances are parametric functions of known regressors. Second order expansions are derived for a class of estimators which includes normal theory maximum likelihood and generalized least squares. The result is a fairly precise description of when conventional asymptotic variance formulae are optimistic; i.e., they underestimate the true variances effectively, this optimism persists for all but heavy-tailed error distributions. We find that maximum likelihood and generalized least squares have the same covariance matrix to second order. Our results also indicate the effect of preliminary estimators .