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In this paper, we present a consistent procedure to assess the significanceof gravitational wave events observed by laser interferometric gravitationalwave detectors based on the background distribution of detection statistic. Wepropose a non-parametric method to estimate $p$-value. Based on the estimated$p$-values, we propose a new procedure to assess the significance of aparticular event with $q$-value which is the minimum false discovery rate thatcan be attained when calling the event significant. The $q$-value gives us acriterion on the significance of events which is different from $P_{\rm astro}$which is used in the LIGO-Virgo analysis and in other analysis. The proposedprocedure is applied to the 1-OGC and 2-OGC catalogs [2][3]. For most of theevents which were claimed significant in [2] and [3], we also obtain the sameresults. However, there are differences in the significance for severalmarginal events. Since the proposed procedure does not require any assumptionson signal and noise, it is very simple and straightforward. The procedure isalso applicable to other searches for gravitational waves whose backgrounddistribution of detection statistic is difficult to know.

A nonparametric method to assess significance of events in search for gravitational waves with false discovery rate