Improving weighted least-squares estimates in heteroscedastic linear regression when the variance is a function of the mean response

In this paper we consider a heteroscedastic linear regression model in which heteroscedasticity is modeled as a smooth function of the linear response. We first construct estimates that are asymptotically equivalent to the weighted least-squares estimate. Then we use the information about the regression parameter contained in the heteroscedasticity to construct estimates that improve upon these estimates under additional assumptions.