Quantile Estimation with Adaptive Importance Sampling

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 the law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with non-unique quantiles, thereby extending the work of Feldman and Tucker [13]. We illustrate the algorithm with an example from credit portfolio risk analysis.