The asymptotic distribution of the unconditional quantile estimator under dependence

Abstract

This paper studies the asymptotic behaviour of the unconditional quantile estimator for dependent random variables. Our proof is based on results from convex stochastic optimization and a mixing process which is specific to quantile estimation and requires only a small part of the σ-algebra generated by the random variable under consideration. The joint asymptotic distribution of several quantiles is given.