ALGORITHM 2.

Monte Carlo sensitivity analysis: confidence intervals

1:	Calculate ${\widehat{p}}_K={\mathbb{P}}_n𝕀\left\{n{\left({\mathit{H}}_{K,\psi }^T{\widehat{\psi }}_K^{\text{adj}}\right)}^2\le {\mathit{H}}_{K,\psi }^T{\widehat{\text{Σ}}}_{{\psi }_K}{\mathit{H}}_{K,\psi }{\chi }_{1,1-\nu }^2\right\}$ where ${\widehat{\text{Σ}}}_{{\psi }_K}$ denotes an estimate of $n\text{Cov}\left({\widehat{\psi }}_K,{\widehat{\psi }}_K\right)$
2:	Calculate resample size ${\widehat{m}}_K=n^{\frac{1+\kappa \left(1-{\widehat{p}}_K\right)}{1+\kappa }}$
3:	for $k=K-1,\dots ,1$ do
4:	Draw $B$ bootstrap samples of size ${\widehat{m}}_k$
5:	Estimate ${\widehat{\psi }}_{k,{\widehat{m}}_k}^{\text{adj},(b)}$ for $b=1,\dots ,B$
6:	For each given ${\mathit{H}}_{k,\psi }={\mathit{h}}_{k,\psi }$, construct a confidence interval for ${\mathit{h}}_{k,\psi }^T{\psi }_k^{\text{adj}}$
7:	Calculate ${\widehat{p}}_k$ by the proportion of confidence intervals for ${\mathit{h}}_{k,\psi }^T{\psi }_k^{\text{adj}}$ that contain zero
8:	Calculate the resample size ${\widehat{m}}_k=n^{\frac{1+\kappa \left(1-p_k\right)}{1+\kappa }}$
9:	end for
10:	Calculate $\widehat{p}={\max }_k{\widehat{p}}_k$ and $\widehat{m}=n^{\frac{1+\kappa (1-p)}{1+\kappa }}$
11:	Draw $B$ bootstrap sample of size $\widehat{m}$
12:	Estimate ${\widehat{\psi }}_{k,\widehat{m}}^{\text{adj},(b)}$ for $k=K,\dots ,1$, $b=1,\dots ,B$
13:	Calculate ${\vartheta }_k/2\times 100$ and $\left(1-{\vartheta }_k/2\right)\times 100$ percentiles of $\sqrt{\widehat{m}}\left({\widehat{\psi }}_{k,\widehat{m}}^{\text{adj},(b)}-{\widehat{\psi }}_k^{\text{adj}}\right)$ which we denote by ${\widehat{l}}_k$ and ${\widehat{u}}_k$ respectively for $k=1,\dots ,K$
14:	Calculate a confidence interval for ${\psi }_k$ by $\left({\widehat{\psi }}_k^{\text{adj}}-{\widehat{u}}_k/\sqrt{\widehat{m}},{\widehat{\psi }}_k^{\text{adj}}+{\widehat{l}}_k/\sqrt{\widehat{m}}\right)$ for $k=K,\dots ,1$