  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.
