New measures of robustness in rare event simulation

Rare event simulation requires acceleration techniques in order to i) observe the rare event and ii) obtain a valid and small confidence interval for the expected value. A "good" estimator has to be robust when rarity increases. This paper aims at studying robustness measures, the standard ones in the literature being Bounded Relative Error and Bounded Normal Approximation. By considering the problem of estimating the reliability of a static model for which simulation time per run is the critical issue, we show that actually those measures do not validate the satisfying behavior of some techniques. We thus define Bounded Relative Efficiency and generalized bounded normal approximation properties of the two previous measures in order to encompass the simulation time. We also illustrate how a user can have a look at the coverage of the resulting confidence interval by using the so-called coverage function.