Optimal design of experiments for correlated processes is an increasingly relevant and active research topic. Present methods have restricted possibilities to judge their quality. To fill this gap, we complement the virtual noise approach by a convex formulation leading to an equivalence theorem comparable to the uncorrelated case and to an algorithm giving an upper performance bound against which alternative design methods can be judged. Moreover, a method for generating exact designs follows naturally. We exclusively consider estimation problems on a finite design space with a fixed number of elements. A comparison on some classical examples from the literature as well as a real application is provided.
翻译:相关过程实验的最佳设计是一个日益相关和积极的研究课题。目前的方法限制了判断其质量的可能性。为了填补这一空白,我们用一个曲线式的配方来补充虚拟噪声方法,这种配方可以使等同的理论与不相关案例相仿,并使算法具有最高性能,可以据此判断替代设计方法。此外,产生精确设计的方法自然而然地随之而来。我们专门考虑用固定数量元素来估计有限设计空间的估算问题。我们比较了文献中的一些典型例子以及实际应用。