First, we apply LD score regression to normalize the test statistics. Under the LCV model, the marginal effect sizes for each trait, α1 and α2, have unit variance. We use a slightly modified version of LD score regression[19] with LD scores computed from UK10K data [58]. In particular, we run LD score regression using a slightly different weighting scheme, matching the weighting scheme in our mixed fourth moment estimators; the weight of SNP i was: (5)wi=1max(1,ℓiHapMap) where ℓiHapMap was the estimated LD score between SNP i and other HapMap3 SNPs (this is approximately the set of SNPs that were used in the regression). This weighting scheme is motivated by the fact that SNPs with high LD to other regression SNPs will be over-counted in the regression (see ref. 19).
