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

We discuss the robust data analysis method to detect a stochastic background of gravitational waves in the presence of non-Gaussian noise. Fundamental methodology to detect weak stochastic signals is to use the cross-correlation statistic which combines the outputs of two gravitational detectors. Usually, the so-called standard cross-correlation (SCC) statistic is used for the data analysis of gravitational-wave background search, which is optimal only if the detector noise obeys a stationary Gaussian process. Here, we consider a {\it generalized cross-correlation} (GCC) statistic, which is nearly optimal even in the presence of non-Gaussian noise. The detection efficiency and the general tendency of the GCC statistic are investigated analytically, particularly focusing on the statistical quantities of the false-alarm and the false-dismissal probabilities and the minimum detectable amplitude of gravitational-wave signals. We find that the GCC statistics is robust against the non-Gaussian tail of detector noises. The detection efficiency of the GCC statistic roughly corresponds to the one of the SCC statistics neglecting the contribution of non-Gaussian tails. These remarkable properties are also checked and confirmed by performing the Monte Carlo simulations