多重混料系统及其最优设计

Multi-Mixture System and Its Optimal Experimental Design

摘要: 本文主要讨论了多重混料系统上Scheff\'{e}模型的最优设计问题. 在本文中, 提出并证明了一个基于单纯形和正定二次型的不等式, 并应用这个不等式解决了多重混料系统上多项式模型的$D$-最优和$A$-最优设计的结构问题, 找到了一个构造最优设计的新方法.
- Scheff\'{e}模型 /
- $D$-最优设计 /
- $A$-最优设计 /
- 单纯形 /
- 多重混料系统
Abstract: In this paper, we discuss some issues of $D$-optimal and $A$-optimal design for Scheff\'{e} model on multiple mixture system. An important inequality based on positive definite quadratic form is also given. Employing the inequality, the structures of optimal designs for Scheff\'{e} model defined on multiple mixture system are made explicit.
- Scheff\'{e} model /
- $D$-optimal design /
- $A$-optimal design /
- simplex form /
- multiple mixture system