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April 2010 Quantile estimation with adaptive importance sampling
Daniel Egloff, Markus Leippold
Ann. Statist. 38(2): 1244-1278 (April 2010). DOI: 10.1214/09-AOS745

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.

Citation

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Daniel Egloff. Markus Leippold. "Quantile estimation with adaptive importance sampling." Ann. Statist. 38 (2) 1244 - 1278, April 2010. https://doi.org/10.1214/09-AOS745

Information

Published: April 2010
First available in Project Euclid: 19 February 2010

zbMATH: 1183.62141
MathSciNet: MR2604712
Digital Object Identifier: 10.1214/09-AOS745

Subjects:
Primary: 62L20, 65C05
Secondary: 65C60

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 2 • April 2010
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