A Semi-Parametric Approach to the Detection of Non-Gaussian
  Gravitational Wave Stochastic Backgrounds
  Using a semi-parametric 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 non-normally
distributed gravitational wave stochastic backgrounds. 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.
