区组试验的稳健设计
Robust designs for experiments with blocks
摘要：
对于在田间小区中或随时间运行的实验，由于空间或序列相关性，观察结果通常是相关的，这导致分析处理平均值的线性模型中的相关误差。如果不知道误差的确切相关矩阵，就不可能计算处理均值的广义最小二乘估计量并使用它来构建实验的最优设计。在本文中，我们建议使用邻域来模拟误差的协方差阵，并应用一个修改的广义最小二乘估计器来构造具有区组的试验的稳健设计。研究了极小极大设计准则，并提出了求解稳健设计的模拟退火算法。我们已经推导出几个理论结果，并提出了代表性的例子。
英文摘要：
For experiments running in field plots or over time, the observations are often correlated due to spatial or serial correlation, which leads to correlated errors in a linear model analyzing the treatment means. Without knowing the exact correlation matrix of the errors, it is not possible to compute the generalized least squares estimator for the treatment means and use it to construct optimal designs for the experiments. In this paper we propose to use neighbourhoods to model the covariance matrix of the errors, and apply a modified generalized least squares estimator to construct robust designs for experiments with blocks. A minimax design criterion is investigated, and a simulated annealing algorithm is developed to find robust designs. We have derived several theoretical results, and representative examples are presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
