二阶可加混料模型稳健D-最优设计

Robust D-optimal Designs of Second-degree Additive Mixture Model

本文研究了在给定两个随机模型先验测度r下的q分量二阶可加混料模型稳健D-最优设计。依据Kiefer次序下完备集的结果且结合稳健D-最优准则,给出了二阶可加模型稳健D-最优的相关理论,并得到了四分量可加模型稳健D-最优ξα_r~*=α_r~*ξ_1~*+(1-α_r~*)ξ_2~*,且利用等价性定理证明了ξα_r~*为稳健D-最优设计。同时基于α_r~*与先验测度r的关系,介绍了先验测度r选择的效率最大最小原则,得到了四分量二阶可加模型的最优先验测度r~*,且比较了四分量二阶可加混料模型稳健D-最优设计与D-最优设计的效率。

Abstract： In this paper, we investigate the robust D-optimal designs of second degree additive mixture model under given prior of two random models. By using complete class result under Kiefer order and robust D-optimal criterion, we give the robust D-optimal theory and gain the robust D-optimal designs ξαr^＊=αr^＊ξ1^＊＋（1-αr^＊）ξ2^＊ of four component additive model. Also, we prove ξαr^＊; is robust D- optimal designs by using equivalence theorem and based on the relationship of αr^＊ and r, we introduce the maximin efficiencies principle and gain the optimal prior r^＊ of four component additive model. Also, we compare the robust D-optimal designs with D-optimal designs about the efficiency of seconde-degree additive mixture model.