For each SNP j, given ∑j, the matrix Ω is estimated using the method of moments (see the Supplementary Note for discussion of the relationship to GMM). For each (t,s)th entry of Ω, ωts, we use the moment condition E(β^j,tβ^j,s−ωts−∑j,ts)=0. This moment condition is derived from observing that E(β^j,tβ^j,s)=E[(βj,t+εj,t)(βj,s+εj,s)]=E[βj,tβj,s]+E[εj,tεj,s]=ωts+∑j,ts. The estimator simply replaces the population expectation with the sample mean:
