Optimality VIS-À-VIS robustness in mixture models with heteroscedastic error

Abstract

Mixture models and designs are used in situations where the response depends on the proportions of the factors (components). Optimum designs were derived for mixture models with fixed regression parameters under homoscedastic error variance by several authors. In this paper, an attempt has been made to find D- and A-optimum designs for the estimation of model parameters with heteroscedastic error variance. It is assumed that the error variance has constant value for all points equidistant from the center of the design. Equivalence theorem plays an important role in this investigation. Robustness of the standard optimum designs in the homoscedastic case under changes in the error variances has also been studied.