  The multi-detector F-statistic is close to optimal for detecting continuous
gravitational waves (CWs) in Gaussian noise. However, it is susceptible to
false alarms from instrumental artefacts, for example quasi-monochromatic
disturbances ('lines'), which resemble a CW signal more than Gaussian noise. In
a recent paper [Keitel et al 2014, PRD 89 064023], a Bayesian model selection
approach was used to derive line-robust detection statistics for CW signals,
generalising both the F-statistic and the F-statistic consistency veto
technique and yielding improved performance in line-affected data. Here we
investigate a generalisation of the assumptions made in that paper: if a CW
analysis uses data from two or more detectors with very different
sensitivities, the line-robust statistics could be less effective. We
investigate the boundaries within which they are still safe to use, in
comparison with the F-statistic. Tests using synthetic draws show that the
optimally-tuned version of the original line-robust statistic remains safe in
most cases of practical interest. We also explore a simple idea on further
improving the detection power and safety of these statistics, which we however
find to be of limited practical use.
