Quantile estimation with adaptive importance sampling
Daniel Egloff, Markus Leippold
The Annals of Statistics · 2010 · Volume 38 · Issue 2
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.
Keywords
62L20, 65C05, 65C60, Adaptive importance sampling, Law of iterated logarithm, Quantile estimation, Robbins–Monro, stochastic approximation
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