Algorithm 3.

Iterative ReMLE

1:	Initialize:
	For $j=1,\dots ,d$
	$\theta \leftarrow 0$
	$y_j^{(\mathbf{\text{crt}})}\leftarrow y_j-\theta =y_j$
	${\beta }_j\leftarrow \text{ReML}(y_j^{(\mathbf{crt})})=\mathbf{\text{ReML}}(y_j)$
2:	while not converge do
3:	$\theta \leftarrow \frac{1}{d}{\sum }_{j=1}^d\left(y_j-X{\beta }_j\right)$
4:	${\mathbf{y}}_{\mathbf{\text{j}}}^{\left(\mathbf{\text{crt}}\right)}{\mathbf{y}}_{\mathbf{\text{j}}}-\theta$
5:	${\beta }_j\leftarrow \text{ReML}({\mathbf{y}}_{\mathbf{\text{j}}}^{\left(\mathbf{\text{crt}}\right)})$
6:	end while