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