Much of the research on multiple comparison and simultaneous inference in the past 60 years or so has been for the comparisons of several population means. Spurrier seems to have been the first to investigate multiple comparisons of several simple linear regression lines using simultaneous confidence bands. In this paper, we extend the work of Liu et al. for finite comparisons of several univariate linear regression models using simultaneous confidence bands to finite comparisons of several multivariate linear regression models using simultaneous confidence tubes. We show how simultaneous confidence tubes can be constructed to allow more informative inferences for the comparison of several multivariate linear regression models than the current approach of hypotheses testing. The methods are illustrated with examples.

中文翻译：

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用于比较多个多元线性回归模型的同时置信管

在过去 60 年左右的时间里，关于多重比较和同时推理的大部分研究都是针对几种总体均值的比较。Spurrier 似乎是第一个使用同时置信带研究几个简单线性回归线的多重比较的人。在本文中，我们扩展了 Liu 等人的工作。用于使用同时置信带的几个单变量线性回归模型的有限比较，以及使用同时置信管的几个多元线性回归模型的有限比较。我们展示了如何构建同时置信管，以允许比当前的假设检验方法为比较多个多元线性回归模型提供更多信息推论。这些方法用例子来说明。