False discovery rate envelope for functional test statistics
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False discovery rate (FDR) is a common way to control the number of false discoveries in multiple testing. In this paper, the focus is on functional test statistics which are discretized into m highly correlated hypotheses and thus resampling based methods are investigated. The aim is to find a graphical envelope that detects the outcomes of all individual hypotheses by a simple rule: the hypothesis is rejected if and only if the empirical test statistic is outside of the envelope. Such an envelope offers a straightforward interpretation of the test results similarly as in global envelope testing recently developed for controlling the family-wise error rate. Two different algorithms are developed to fulfill this aim. The proposed algorithms are adaptive single threshold procedures which include the estimation of the true null hypotheses. The new methods are illustrated by two real data examples.
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