False discovery rate envelopes

Abstract

False discovery rate (FDR) is a common way to control the number of false discoveries in multiple testing. There are a number of approaches available for controlling FDR. However, for functional test statistics, which are discretized into $m$ highly correlated hypotheses, the methods must account for changes in distribution across the functional domain and correlation structure. Further, it is of great practical importance to visualize the test statistic together with its rejection or acceptance region. Therefore, the aim of this paper is to find, based on resampling principles, a graphical envelope that controls FDR and 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 the recently developed global envelope testing which controls the family-wise error rate. Two different adaptive single threshold procedures are developed to fulfill this aim. Their performance is studied in an extensive simulation study. The new methods are illustrated by three real data examples.

References in corpus (6)

• Global envelope tests for spatial processes
• Multiple testing with discrete data: proportion of true null hypotheses and two adaptive FDR procedures
• False discovery rate control for multiple testing based on p-values with càdlàg distribution functions
• A one-way ANOVA test for functional data with graphical interpretation
• Revisiting the random shift approach for testing in spatial statistics
• Distribution-Free Pointwise Adjusted P-Values for Functional Hypotheses

Cited by in corpus (3)

• Spectral estimation for spatial point processes and random fields
• The power of visualizing distributional differences: Formal graphical $n$-sample tests
• Conformal novelty detection for replicate point patterns with FDR or FWER control