Cross-cumulants measure for independence

We propose a measure for independence of group of random variables, given by a sum of cross-cumulants of a given order n  . A similar measure was known for the case of fourth-order cross-cumulants from the JADE algorithm for ICA (independent component analysis). We derive a formula for its calculation using cumulant tensors. In the case n=4n=4 our formula allows efficient calculation of this measure, using cumulant matrices. Much attention is devoted to the case of six-order cross-cumulants, aiming to show that this measure can be calculated using again cumulant matrices.