Semiparametric approach to the detection of non-Gaussian gravitational wave stochastic backgrounds

Using a semiparametric approach based on the fourth-order Edgeworth expansion for the unknown signal distribution, we derive an explicit expression for the likelihood detection statistic in the presence of a non-normally distributed gravitational wave stochastic background. Numerical likelihood maximization exercises based on Monte Carlo simulations for a set of large tail symmetric non-Gaussian distributions suggest that the fourth cumulant of the signal distribution can be estimated with reasonable precision when the ratio between the signal and the noise variances is larger than 0.01. The estimation of higher-order cumulants of the observed gravitational wave signal distribution is expected to provide additional constraints on astrophysical and cosmological models.