Optimal design of experiments for multivariate response in two-factor linear models
Optimal design of experiments for multivariate response in two-factor linear models
复制标题
二因素线性模型中多变量响应实验的优化设计
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
R. Schwabe
中科院分区：
文献类型：
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作者：
R. Schwabe
|实验设计的目的是根据所选实验条件的设置，优化将要使用的统计程序的某些特性。特别是，最小二乘估计的(渐近)协方差矩阵的某些泛函将被最小化。对于多变量观测，设计实验比单变量设置要复杂得多。如果还有许多影射因素可能以不同的方式相互作用，情况就会变得更糟。然而，通过简化原则，我们能够在多因素环境中为广泛类别的多变量观测生成最优设计，这里将在两个影响因素的情况下说明这一点。
|The design of experiments aims at optimizing certain charcteristics of the statistical procedures to be used, in dependence on the settings for the experimental conditions chosen. In particular, certain functionals of the (asymptotic) covariance matrix of the least squares estimator are to be minimized. For multivariate observations designing experiments is substantially more complicated than in univariate settings. If there are additionally many factors of innuence which may interact in diierent ways, the situation becomes even worse. However, by reduction principles, we are able to generate optimal designs for broad classes of multivariate observations in multi-factor settings which will be illustrated here in the case of two factors of innuence.