In this paper we describe a coherent multiple testing procedure for correlated test statistics such as are encountered in functional linear models. The procedure makes use of two different \(p\) value combination methods: the Fisher combination method and the Šidák correction-based method. \(p\) values for Fisher’s and Šidák’s test statistics are estimated through resampling to cope with the correlated tests. Building upon these two existing combination methods, we propose the smallest \(p\) value as a new test statistic for each hypothesis. The closure principle is incorporated along with the new test statistic to obtain the overall \(p\) value and appropriately adjust the individual \(p\) values. Furthermore, a shortcut version for the proposed procedure is detailed, so that individual adjustments can be obtained even for a large number of tests. The motivation for developing the procedure comes from a problem of point-wise inference with smooth functional data where tests at neighboring points are related. A simulation study verifies that the methodology performs well in this setting. We illustrate the proposed method with data from a study on the aerial detection of the spectral effect of below ground carbon dioxide leakage on vegetation stress via spectral responses.

中文翻译：

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基于重采样的多重比较程序，适用于功能数据的逐点测试。

在本文中，我们为相关的测试统计数据（如功能线性模型中遇到的）描述了一个连贯的多重测试程序。该过程使用两种不同的\（p \）值组合方法：Fisher组合方法和基于Šidák校正的方法。Fisher和Šidák的检验统计量的\（p \）值通过重新采样来估计，以应对相关检验。在这两种现有组合方法的基础上，我们针对每个假设提出最小的\（p \）值作为新的检验统计量。将闭包原理与新的测试统计信息结合在一起，以获得总体\（p \）值并适当地调整单个\（p \）价值观。此外，还详细介绍了所建议过程的快捷方式，因此即使对于大量测试也可以进行单独调整。开发该程序的动机来自于使用平滑功能数据进行逐点推理的问题，其中相邻点的测试相关。仿真研究验证了该方法在这种情况下的性能良好。我们通过对地下二氧化碳泄漏通过光谱响应对植被胁迫的光谱效应进行空中检测的研究数据来说明所提出的方法。