Algorithm 1.

reREHE Approach Estimation.

for $b=1$ to $B$ do

(a) Sample with replacement from $Y$ to obtain a length $\left[n{r}_s\right]$ vector $Y^{\left(b\right)}$ with sampling rate $r_s$, where $\left[x\right]$ is a function to round $x$ to the nearest integer; subset the correlation matrices accordingly as $D_k^{\left(b\right)}$, for $k=0,1.$

(b) Compute the variance component estimates $\left({\tilde{\sigma }}_{0,re}^{2\left(b\right)},{\tilde{\sigma }}_{1,re}^{2\left(b\right)}\right)$ based on $Y^{\left(b\right)}$ and $D_k^{\left(b\right)}$’s using REHE [4].

end for

Estimate the variance components as ${\tilde{\sigma }}_{k,re}^2=\frac{1}{B}\sum _{b=1}^B{\tilde{\sigma }}_{k,re}^{2\left(b\right)},k=0,1.$