On signal detection using the Benjamini-Hochberg procedure

Abstract

We investigate a multiple hypothesis test designed for detecting signals embedded in noisy observations of a sensor array. The global level of the multiple test is controlled by the false discovery rate (FDR) criterion recently sugaested by Benjamini and Hochberg instead of the classical familywise error rate (FWE) criterion. In the previous study [3], the suggested procedure has shown promising results oil simulated data. Here we carefully examine the independence condition required by the Benjamini Hochberg procedure to ensure the control of FDR. Based oil the properties of beta distribution, we proved the applicability of the Benjamini Hochberg procedure to the underlying test. Further simulation results show that the false alarm rate is less than 0.02 for a choice of FDR as high as 0.1, implying the reliability of the test has not been affected by the increase in power.