Robust Estimation in Heteroscedastic Linear Models

We consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter θ. We propose robust estimates for the regression parameter β and show that, as long as a reasonable starting estimate of θ is available, our estimates of β are asymptotically equivalent to the natural estimate obtained with known variances. A particular method for estimating θ 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 β.