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The asymptotic distribution of the unconditional quantile estimator under dependence

Oberhofer, Walter ; Haupt, Harald



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.


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