Residual variance model parameter estimation using weighted

RESIDUAL VARIANCE MODEL PARAMETER ESTIMATION USING WEIGHTED LEAST-SQUARES... 

Carroll and Ruppert (1988) and Davidian and Gil-tinan (1995) present comprehensive overviews of parameter estimation in the face of heteroscedasticity. In general, three methods are used to provide precise, unbiased parameter estimates weighted least-squares (WLS), maximum likelihood, and data and/or model transformations. Johnston (1972) has shown that as the departure from constant variance increases, the benefit from using methods that deal with heteroscedasticity increases. The difficulty in using WLS or variations of WLS is that additional burdens on the model are made in that the method makes the additional assumption that the variance of the observations is either known or can be estimated. In WLS, the goal is not to minimize the OLS objective function, i.e., the residual sum of squares,... 

Small variances guarantee that the parameter is accurately estimated and small correlation coefficients indicate that the parameters camiot be mutually compensated. The variances are very much dependent on the precision of the experiments since they are directly proportional to the weighted sum of residual squares (Q), while the correlation coefficient depends heavily on the model structure as such. Special tricks to suppress the correlation between parameters exist, and should always be used. 

---