We consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter $\theta$. We propose robust estimates for the regression parameter $\beta$ and show that, as long as a reasonable starting estimate of $\theta$ is available, our estimates of $\beta$ are asymptotically equivalent to the natural estimate obtained with known variances. A particular method for estimating $\theta$ is proposed and shown by Monte-Carlo to work quite well, especially in power and exponential models for the variances. We also briefly discuss a "feedback" estimate of $\beta$.
Raymond J. Carroll. David Ruppert. "Robust Estimation in Heteroscedastic Linear Models." Ann. Statist. 10 (2) 429 - 441, June, 1982. https://doi.org/10.1214/aos/1176345784