A-Optimal designs for mixture polynomial models with heteroscedastic errors

Abstract

This paper searches $ A $-optimal designs for mixture polynomial models when the errors are heteroscedastic. Sufficient conditions are given so that $ A $-optimal designs for the complex mixture polynomial models can be constructed from the direct sum of $ A $-optimal designs for their sub-mixture models with different structures of heteroscedasticity. Several examples are presented to further illustrate and check optimal designs based on $ A $-optimality criterion.

Keywords

• mixture experiments
• heteroscedasticity
• $ a $-optimal design
• mixture polynomial models
• direct sum design