Table S1 shows estimates from 1000 simulations compared to the analytic values, for the three estimators discussed. Mean square error for the allele count estimator is not meaningful without further scaling of the polygenic score, which is a further problem not of present interest. All simulations agree well with the analytic results. Because the variances and covariance are bounded in (0,1), their median estimates are shown with the coverage, rather than their means. The proposed estimating equations are seen to be accurate, but the confidence intervals are anti-conservative when the number of markers with effects is low, here 1000. This is because the realised variance and covariance in equation 7 depart from their large m expectation, with resulting over-dispersion in the estimating equation (left hand side of equation 6). However when the number of markers with effects is 5000, the correct coverage is attained.
