Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic

摘要

We discuss a robust data analysis method to detect a stochastic background ofgravitational waves in the presence of non-Gaussian noise. In contrast to thestandard cross-correlation (SCC) statistic frequently used in the stochasticbackground searches, we consider a {\it generalized cross-correlation} (GCC)statistic, which is nearly optimal even in the presence of non-Gaussian noise.The detection efficiency of the GCC statistic is investigated analytically,particularly focusing on the statistical relation between the false-alarm andthe false-dismissal probabilities, and the minimum detectable amplitude ofgravitational-wave signals. We derive simple analytic formulae for thesestatistical quantities. The robustness of the GCC statistic is clarified basedon these formulae, and one finds that the detection efficiency of the GCCstatistic roughly corresponds to the one of the SCC statistic neglecting thecontribution of non-Gaussian tails. This remarkable property is checked byperforming the Monte Carlo simulations and successful agreement betweenanalytic and simulation results was found.