I am reading some paper about high-order statistics https://link.springer.com/article/10.1007%2Fs11004-009-9258-9?LI=true. The paper gives two recursive expressions relating the multivariate cumulants to moments, as shown in first and second attached figures. Also the expressions of cumulants expressed as moments are given directly (i.e. c1,2,3, c1,2,3,4).
I want to derive the expression of multivariate cumulant from the recursive relation. But I am stuck with even the derivation of bivariate cumulant (Figure 3).
Is there someone familiar with the high-order statistics? Please give me some help to get out? Thank you.
