Algorithm 3. Bootstrap confidence interval

$$\begin{gathered} \begin{array}{cc}\hfill & \mathrm{Input}:\text{matrices:}X,Z\text{and}Q,\text{column matrix of responses:}y,\text{optimal parameters:}{\lambda }_Q\text{and}{\lambda }_R,\hfill \\ \hfill & \text{the number of bootstrap samples:}s(\text{by defaults}s=500)\hfill \\ \hfill & \mathbf{For}j\in (1,\dots ,k)\mathrm{do}:\hfill \\ \hfill & \\ 1.\text{generate}j\text{th bootstrap sample},X^{[j]},Z^{[j]}\text{and}{y}^{[j]},\text{by sampling with replacement from}\hfill \\ \hfill & [X,Z,y]\hfill \\ \hfill & \\ 2.\text{get}j\text{th griPEER estimate},{\widehat{\mathcal{B}}}^{[j]},\text{for}Q,X^{[j]},Z^{[j]},y^{[j]}\text{and tuning parameters}{\lambda }_Q\text{and}{\lambda }_R\hfill \\ \hfill & \mathbf{End}\hfill \\ \hfill & \text{Define}C{I}_{boot}({\mathcal{B}}_i)-\text{the bootstrap CI for}{\mathcal{B}}_i-\text{as the percentile bootstrap confidence interval}\hfill \\ \hfill & \text{for}{\widehat{\mathcal{B}}}_i^{[1]},\dots ,{\widehat{\mathcal{B}}}_i^{[s]}\text{with the significance level}\alpha =0.05\hfill \end{array} \end{gathered}$$