I have calculated the confidence intervals of the VaR for two assets using iid bootstrap. I compute VaR using historical simulation (non-parametric). So I have two bootstrap confidence intervals (in my case percentile intervals). How can I infer on them? For example, let's say that the two intervals are overlapped: can I say that they represent the same VaR (thus the same risk)? And if they are not overlapped? Do you know if there is some statistical test useful in this case?