Quantile estimation with adaptive importance sampling
Statistics Theory
2010-03-01 v1 Statistics Theory
Abstract
We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with nonunique quantiles thereby extending the work of Feldman and Tucker [Ann. Math. Statist. 37 (1996) 451--457]. We illustrate the algorithm with an example from credit portfolio risk analysis.
Cite
@article{arxiv.1002.4946,
title = {Quantile estimation with adaptive importance sampling},
author = {Daniel Egloff and Markus Leippold},
journal= {arXiv preprint arXiv:1002.4946},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.1214/09-AOS745 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)