Bounded Relative Efficiency in Rare Event Simulation

This paper investigates the robustness of rare event simulation estimators when rarity increases. The literature had up to now focused on bounded relative error (BRErr) or bounded normal approximation properties stating respectively that the relative size and the coverage error of the confidence interval are bounded whatever the rarity is. Using a reliability estimation problem, we show that there exists some efficient estimators for which BRErr is not verified. The efficiency is due to the fact that the number of estimations during a given simulation time increases with the rarity. We thus define a property called bounded relative efficiency ecompassing the examples of estimators verifying BRErr, and representing the actual property an analyst has to look at.