In a heteroscedastic linear model, we establish the asymptotic normality of the iterative weighted least squares estimators with weights constructed by using the within-group residuals obtained from the previous model fitting. An adaptive procedure is proposed which ensures that the iterative process stops after a finite number of iterations and produces an estimator asymptotically equivalent to the best estimator that can be obtained by using the iterative procedure. Theoretical and empirical results of the performance of the adaptive estimator are presented.
"Iterative Weighted Least Squares Estimators." Ann. Statist. 21 (2) 1071 - 1092, June, 1993. https://doi.org/10.1214/aos/1176349165