Iterative weighted least-squares estimates in a heteroscedastic linear regression model

The aim of this study is to improve the efficiency of weighted least-squares estimates for a regression parameter. An iterative procedure, starting with an unbiased estimate other than the unweighted least-squares estimate, yields estimates which are asymptotically more efficient than the feasible generalized least-squares estimate when errors are spherically distributed. The result has an application in the improvement of the Graybill–Deal estimate of the common mean of several normal populations.