Extracting Information from the Variance Function: Optimal Design

Regression models with the variance function depending on unknown parameters appear in a number of practical problems (variogram fitting and mixed effect models are popular examples). We found that estimation of parameters entering both response and variance functions can be combined in a rather simple way. The proposed estimator belongs to the class of iterated estimators and is numerically very close to the fixed point method, which takes the form of the reweighted least squares method in our setting. The proposed estimators lead to design problems with additive information matrices and therefore can be treated within traditional convex design theory.