最佳行列设计

IF 2.4 2区数学 Q2 BIOLOGY

Biometrika Pub Date : 2022-08-10 DOI:10.1093/biomet/asac046

Zheng Zhou, Yongdao Zhou

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引用次数: 0

摘要

行-列设计已被广泛用于涉及双重混杂的实验中。其中，对所有主要影响和尽可能多的双因素相互作用提供无条件估计的方法是优选的，并被称为最优方法。目前的大多数工作都集中在两层行列设计的构建上，而相应的最优性理论在很大程度上被忽视了。此外，大多数构建的设计至少包含一个全因子设计的副本，随着因子数量的增加，这是不灵活的。在本研究中，建立了一个理论框架来评估具有素数水平的行-列设计的最优性。提出了一种构造具有素数级的最优行列设计的方法。随后，对于任何参数组合，构造了最优的全阶乘三电平行列设计。为了节省成本，还构造了最优的分数因子两级和三级行列设计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Optimal Row-Column Designs

Row-column designs have been widely used in experiments involving double confounding. Among them, one that provides unconfounded estimation of all main effects and as many two-factor interactions as possible is preferred, and is called optimal. Most current work focuses on the construction of two-level row-column designs, while the corresponding optimality theory has been largely ignored. Moreover, most constructed designs contain at least one replicate of a full factorial design, which are not flexible as the number of factors increases. In this study, a theoretical framework is built up to evaluate the optimality of row-column designs with prime level. A method for constructing optimal row-column designs with prime level is proposed. Subsequently, optimal full factorial three-level row-column designs are constructed for any parameter combination. Optimal fractional factorial two-level and three-level row-column designs are also constructed for cost-saving.

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来源期刊

Biometrika 生物-生物学

CiteScore

5.50

自引率

3.70%

发文量

审稿时长

6-12 weeks

期刊介绍： Biometrika is primarily a journal of statistics in which emphasis is placed on papers containing original theoretical contributions of direct or potential value in applications. From time to time, papers in bordering fields are also published.