Quantile estimation with adaptive importance sampling

Details Quantile estimation with adaptive importance sampling Quantile estimation with adaptive importance sampling

2010-02-26

arxiv.org/abs/1002.4946v1

Annals of Statistics 2010, Vol. 38, No. 2, 1244-1278

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS745 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS745

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.

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