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arXiv · 1002.4946

Quantile estimation with adaptive importance sampling

Daniel Egloff·Markus Leippold
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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.

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Daniel Egloff, Markus Leippold. 2010-02-26. Quantile estimation with adaptive importance sampling. https://doi.org/10.1214/09-aos745

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