In the second line, we used the independence assumption to discard cross-terms of the form γpπ3 and γ13π, and we used the symmetry assumption to discard terms of the form γ1γ23. In the third and fourth lines, we used the independence assumption, which implies that E(γ12π2)=E(γ12)E(π2)=E(γ12)=1−q12. The factor E(π4) – 3 is the excess kurtosis of π , which is zero when π follows a Gaussian distribution; in order for the estimation equation to be useful, E(π4) – 3 must be nonzero (see Supplementary Note).
