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The multi-detector F-statistic is close to optimal for detecting continuousgravitational waves (CWs) in Gaussian noise. However, it is susceptible tofalse alarms from instrumental artefacts, for example quasi-monochromaticdisturbances ('lines'), which resemble a CW signal more than Gaussian noise. Ina recent paper [Keitel et al 2014, PRD 89 064023], a Bayesian model selectionapproach was used to derive line-robust detection statistics for CW signals,generalising both the F-statistic and the F-statistic consistency vetotechnique and yielding improved performance in line-affected data. Here weinvestigate a generalisation of the assumptions made in that paper: if a CWanalysis uses data from two or more detectors with very differentsensitivities, the line-robust statistics could be less effective. Weinvestigate the boundaries within which they are still safe to use, incomparison with the F-statistic. Tests using synthetic draws show that theoptimally-tuned version of the original line-robust statistic remains safe inmost cases of practical interest. We also explore a simple idea on furtherimproving the detection power and safety of these statistics, which we howeverfind to be of limited practical use.

Line-robust statistics for continuous gravitational waves: safety in the case of unequal detector sensitivities