Algorithm 3.

riPEER

input: matrices Z, X, positive semi-definite matrix Q

1: find SVD of Q, i.e. Q =USU⊤;

2: define projection matrix ${\mathcal{P}}_X^c$ as ${\mathcal{P}}_X^c:=I_n-X{(X^{\top }X)}^{-1}{X}^{\top }$;

3: denote $y_{\mathcal{P}}:={\mathcal{P}}_X^{c}y,Z_{\mathcal{P}};={\mathcal{P}}_X^{c}Z,\stackrel{\sim }{Z}:={\mathcal{P}}_X^{c}ZU$;

4: find estimates of λQ and λR by solving optimization problem in (3.7);

5: define ${\widehat{b}}^{\text{rP}}:={(Z_{\mathcal{P}}^{\top }{Z}_{\mathcal{P}}+{\lambda }_{Q}Q+{\lambda }_R{I}_P)}^{-1}{Z}_{\mathcal{P}}^{\top }{y}_{\mathcal{P}}$, β̂rP := (X⊤X)−1X⊤(y−Z)b̂rP.