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.
Publié le : 2010-04-15
Classification:
Quantile estimation,
law of iterated logarithm,
adaptive importance sampling,
stochastic approximation,
Robbins–Monro,
62L20,
65C05,
65C60
@article{1266586629,
author = {Egloff, Daniel and Leippold, Markus},
title = {Quantile estimation with adaptive importance sampling},
journal = {Ann. Statist.},
volume = {38},
number = {1},
year = {2010},
pages = { 1244-1278},
language = {en},
url = {http://dml.mathdoc.fr/item/1266586629}
}
Egloff, Daniel; Leippold, Markus. Quantile estimation with adaptive importance sampling. Ann. Statist., Tome 38 (2010) no. 1, pp. 1244-1278. http://gdmltest.u-ga.fr/item/1266586629/