On the background estimation by time slides in a network of gravitational wave detectors

Time shifting the outputs of Gravitational Wave detectors operating in coincidence is a convenient way to estimate the background in a search for short duration signals. However this procedure is limited as increasing indefinitely the number of time shifts does not provide better estimates. We show that the false alarm rate estimation error saturates with the number of time shifts. In particular, for detectors with very different trigger rates this error saturates at a large value. Explicit computations are done for 2 detectors, and for 3 detectors where the detection statistic relies on the logical ``OR of the coincidences of the 3 couples in the network.