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
