To produce unbiased SE estimates and test statistics, we require the sampling covariance matrix, VSLDSC, of the LDSC estimates that is composed of all nonredundant elements in the SLDSC matrix. Thus, it is a symmetric matrix of order k*, with k*(k* +1)/2 nonredundant elements. The diagonal elements of VSLDSC are sampling variances, that is, squared SEs of the elements in SLDSC. The off-diagonal elements of VSLDSC are sampling covariances that indicate the extent to which the sampling distributions of the variance and covariance estimates in SLDSC covary with one another, as would be expected when there is overlap among the samples from which the terms are estimated. This VSLDSC matrix can be written as: VSLDSC=[SE(h12)2cov(h12,σg1,g2)SE(σg1,g2)2⋮⋮⋱cov(h12,σg1,gk)cov(σg1,g2,σg1,gk)SE(σg1,gk)2⋱cov(h12,hj2)cov(σg1,g2,hj2)cov(σg1,gk,hj2)SE(hj2)2⋱cov(h12,σgj,gk)cov(σg1,g2,σgj,gk)cov(σg1,gk,σgj,gk)cov(hj2,σgj,gk)SE(σgj,gk)2cov(h12,hk2)cov(σg1,g2,hk2)cov(σg1,gk,hk2)cov(hj2,hk2)cov(σgj,gk,hk2)SE(hk2)2]
