Figure 2.

Per-Partition Shrinkage Weights Estimated by Non-Parametric Shrinkage (NPS) Approximate the Conditional Mean Effects in the Decorrelated Space

(A) NPS shrinkage weights ${\omega }_k$ (red line) compared to the theoretical optimum (black line), ${\lambda }_{lj}/\left({\lambda }_{lj}+\frac{M}{N_g{h}^2}\right)$, under infinitesimal architecture. The partition of largest eigenvalues ${\mathcal{S}}_{10}$ is marked by gray box.

(B) Conditional mean effects estimated by NPS (red line) in sub-partitions of ${\mathcal{S}}_{10}$ by $\left|{\hat{\eta }}_{lj}\right|$ under infinitesimal architecture. The theoretical line (black) is the average over all ${\lambda }_{lj}$ in ${\mathcal{S}}_{10}$.

(C and D) Conditional mean effects estimated by NPS (red line) in sub-partitions of ${\mathcal{S}}_{10}$ (C) and ${\mathcal{S}}_2$ (D) on intervals of $\left|{\hat{\eta }}_{lj}\right|$ under non-infinitesimal architecture with the causal SNP fraction of 1%. The true conditional means (black) were estimated over 40 simulation runs.

The mean NPS shrinkage weights (red line) and their 95% CIs (red shade) were estimated from five replicates. Grey vertical lines indicate partitioning cut-offs. No shrinkage line (green) indicates ${\omega }_k=1$. The number of markers $M$ is 101,296. The discovery GWAS size $N_g$ equals to $M$. The heritability $h^2$ is 0.5.