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Quantile Estimation with Adaptive Importance Sampling


Leippold, Markus; Egloff, Daniel (2010). Quantile Estimation with Adaptive Importance Sampling. Annals of Statistics, 38(2):1244-1278.

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. We illustrate the algorithm with an example from credit portfolio risk analysis.

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. We illustrate the algorithm with an example from credit portfolio risk analysis.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Language:English
Date:2010
Deposited On:30 Oct 2009 05:36
Last Modified:14 Jul 2020 14:43
Publisher:Institute of Mathematical Statistics
ISSN:0090-5364
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1214/09-AOS745

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