False Discovery Rate Envelope and its Performance for Local Testing in Functional Data Analysis
摘要
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, it is of great practical importance to visualize the test statistic together with its rejection or acceptance region. Therefore, the FDR envelope was introduced based on resampling principles. This graphical envelope 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, similar to the recently developed global envelope testing, which controls the family-wise error rate. Here, I summarise the comparison of the performance of these two envelopes with several procedures designed directly for local testing tasks in functional data analysis. Namely, interval-wise testing, threshold-wise testing, step-down 𝑝-min adjustment, and adaptive two-stage FDR procedure. The comparison is done on the base of a simulation study that consists of 1584 scenarios.