Reanalysis of F-statistic gravitational-wave searches with the higher criticism statistic

We propose a new method of gravitational wave detection using a modified form of higher criticism, a statistical technique introduced by Donoho & Jin (2004). Higher criticism is designed to detect a group of sparse, weak sources, none of which are strong enough to be reliably estimated or detected individually. We apply higher criticism as a second-pass method to synthetic F-statistic and C-statistic data for a monochromatic periodic source in a binary system and quantify the improvement relative to the first-pass methods. We find that higher criticism on C-statistic data is more sensitive by ~6% than the C-statistic alone under optimal conditions (i.e. binary orbit known exactly) and the relative advantage increases as the error in the orbital parameters increases. Higher criticism is robust even when the source is not monochromatic (e.g. phase wandering in an accreting system). Applying higher criticism to a phase-wandering source over multiple time intervals gives a >30% increase in detectability with few assumptions about the frequency evolution. By contrast, in all-sky searches for unknown periodic sources, which are dominated by the brightest source, second-pass higher criticism does not provide any benefits over a first pass search