We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest in this technique for 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. The application to the COBE two-year correlation function reveals a significant displacement of the parameter confidence region with respect to the Gaussian case.