Extreme quantile estimation with nonparametric adaptive importance sampling

In this article, we propose a nonparametric adaptive importance sampling (NAIS) algorithm to estimate rare event quantile. Indeed, Importance Sampling (IS) is a well-known adapted random simulation technique. It consists in generating random weighted samples from an auxiliary distribution rather than the distribution of interest. The optimization of this auxiliary distribution is often very difficult in practice. First, we review how to define the optimal auxiliary density of IS for quantile estimation in the general case and then propose a nonparametric method based on Gaussian kernel density estimator to approach the optimal auxiliary density that does not assume an initial PDF guess. This method is then finally applied to theoretical cases to demonstrate the efficiency of the proposed NAIS algorithm and on the quantile estimation of the temperature of a forest fire detection simulator.