Non-Gaussian Chi-squared method with the multivariate Edgeworth expansion

I present here a generalization of the maximum likelihood method and the $\chi^2$ method to the cases in which the data are {\it not} assumed to be Gaussian distributed. The method, based on the multivariate Edgeworth expansion, can find several astrophysical applications. I mention only two of them. First, in the microwave background analysis, where it cannot be excluded that the initial perturbations are non-Gaussian. Second, in the large scale structure statistics, as we already know that the galaxy distribution deviates from Gaussianity on the scales at which non-linearity is important. As a first interesting result I show here how the confidence regions are modified when non-Gaussianity is taken into account.