Importance sampling for simulations of moderate deviation probabilities of statistics

Summary In recent years importance has become the standard tool for estimation of probabilities of rare events. Of special interest is efficient importance sampling which allows a substantial reduction of the computational burden. Efficiency of importance sampling has been proved (see Sadowsky and Bucklew [19]) under rather strong assumptions, which often cannot be verified for particular test statistics and estimators. In this paper we show that efficient importance sampling correctly works for calculation of moderate deviation probabilities of statistics having influence functions.