Resampling-based multiple comparison procedure with application to point-wise testing with functional data

摘要

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 value combination methods: the Fisher combination method and the idak correction-based method. values for Fisher's and idak's test statistics are estimated through resampling to cope with the correlated tests. Building upon these two existing combination methods, we propose the smallest value as a new test statistic for each hypothesis. The closure principle is incorporated along with the new test statistic to obtain the overall value and appropriately adjust the individual 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.