The construction of universally optimal designs, if such exist, is difficult to obtain, especially when there are some nuisance effects or correlated errors. The hub correlation is a special correlation structure with applications to experiments in genetics, networks and other areas in industry and agriculture. There may be restrictions on the correlation values of the hub structure depending on the experiment. Optimality of block designs under hub correlation has been studied for the case of a constant correlation value. In this article, we consider the hub structure when one of the correlation values is different from the others, and the universally optimal block designs, binary or non‐binary, are theoretically obtained. Also, we introduce an algorithm to construct the optimal designs. The Canadian Journal of Statistics 48: 596–604; 2020 © 2020 Statistical Society of Canada

中文翻译：

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用于相关观测的最佳平衡块设计

如果存在通用优化设计，则很难获得其构造，尤其是当存在一些令人讨厌的影响或相关误差时。集线器相关性是一种特殊的相关性结构，可应用于遗传，网络和工农业的其他领域的实验。根据实验，轮毂结构的相关值可能会受到限制。对于恒定相关值的情况，已经研究了在枢纽相关下的块设计的最优性。在本文中，当相关值之一彼此不同时，我们考虑轮毂结构，并且从理论上获得了通用最优块设计（二进制或非二进制）。此外，我们介绍了一种构建最佳设计的算法。加拿大统计杂志48：596–604；2020©2020加拿大统计学会