Constructions of Φp-optimal rotational designs on the ball
Constructions of Φp-optimal rotational designs on the ball
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球上 Φp 最优旋转设计的构造
DOI：
10.1007/s13171-014-0053-4
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Sawa and M. Jimbo
中科院分区：
文献类型：
--
作者：
M. Hirao;M. Sawa and M. Jimbo
讨论了单位球上3阶Φ p-最优近似设计的两种基本构造方法。一种是基于B型Weyl群下的调和多项式不变理论，另一种是使用统计工具，如区组设计和正交表。本文系统地介绍了Gaffke和Heiligers（1995 a，B，c）及其他研究者在实验设计中常用的群论方法。
We discuss two fundamental methods for constructing Φp-optimal approximate designs of order 3 on the unit ball. One construction is based on the theory of harmonic polynomials invariant under the Weyl group of typeB, and another uses statistical tools such as block designs and orthogonal arrays. The paper provides a systematic treatment of a group-theoretic approach for constructing such designs, which has been traditionally used by Gaffke and Heiligers (1995a, b, c) and other researchers in design of experiments.