Efficient estimation of extreme quantiles using adaptive kriging and importance sampling

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 dif...

Importance Sampling for Monte Carlo Estimation of Quantiles

This paper is concerned with applying importance sampling as a variance reduction tool for computing extreme quantiles. A central limit theorem is derived for each of four proposed importance sampling quantile estimators. EEciency comparisons are provided in a certain asymptotic setting, using ideas from large deviation theory.

Nonparametric Estimation of Extreme Conditional Quantiles

The estimation of extreme conditional quantiles is an important issue in different scientific disciplines. Up to now, the extreme value literature focused mainly on estimation procedures based on i.i.d. samples. On the other hand, quantile regression based procedures work well for estimation within the data range i.e. the estimation of nonextreme quantiles but break down when main interest is i...

Functional nonparametric estimation of conditional extreme quantiles

− We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such ”extreme” quantiles can be located in the range of the data or near and even beyond the boundary of the sample, depending on the convergence rate of their order to one. Nonp...

Quantile Estimation with Adaptive Importance Sampling