Algorithm 1.

Iterative MLE

Initialize:

For $j=1,\dots ,d$

$\theta \leftarrow \mathbf{0}$

$y_j^{(\mathbf{\text{crt}})}\leftarrow y_j-\theta =y_j$

${\beta }_j\leftarrow {\left(X^{T}X\right)}^{-1}{X}^T{y}_j^{(crt)}={\left(X^{T}X\right)}^{-1}{X}^T{y}_j$

while not converge do

$\theta \leftarrow \frac{1}{d}{\sum }_{j=1}^d\left(y_j-X{\beta }_j\right)$

$y_j^{(crt)}\leftarrow y_j-\theta$

${\beta }_j\leftarrow {\left(X^{T}X\right)}^{-1}{X}^T{y}_j^{(crt)}$

end while