Detection of the Number of Signals Using the Benjamini-Hochberg Procedure

Abstract

This paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array. We formulate the detection problem as a multiple hypothesis test. To control the global level of the multiple test, we apply the false discovery rate (FDR) criterion proposed by Benjamini and Hochberg. Compared to the classical familywise error rate (FWE) criterion, the FDR-controling procedure leads to a significant gain in power for large size problems. In addition, we apply the bootstrap technique to estimate the observed significance level required by the FDR-controling procedure. Simulations show that the FDR-controling procedure always provides higher probability of correct detection than the FWE-controling procedure. Furthermore, the reliability of the proposed test procedure is not affected by the gain in power of the test.