Non-Gaussian Likelihood Function

Abstract

We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the determination of a non-Gaussian signature is relevant, e.g. in the analysis of large scale structure and cosmic microwave background. A first important result is that the asymptotic confidence limits on the parameters are systematically widened when the higher order correlation functions are positive, with respect to the Gaussian case.