Quantile estimation with adaptive importance sampling

TL;DR

This paper presents new adaptive importance sampling-based quantile estimators that converge for general distributions, including those with nonunique quantiles, supported by theoretical proofs and an application in credit risk analysis.

Contribution

It introduces novel adaptive quantile estimators using importance sampling and proves their convergence under broad conditions, extending prior work.

Findings

Proved convergence of adaptive quantile estimators for general distributions.

Extended law of iterated logarithm for martingales to this context.

Demonstrated the method with a credit portfolio risk example.

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.