Nonparametric asymptotic confidence intervals for extreme quantiles

In this paper, we propose new asymptotic confidence intervals for extreme quantiles, that is, for quantiles located outside the range of the available data. We restrict ourselves to the situation where the underlying distribution is heavy-tailed. While asymptotic confidence intervals are mostly constructed around a pivotal quantity, we consider here an alternative approach based on the distribution of order statistics sampled from a uniform distribution. The convergence of the coverage probability to the nominal one is established under a classical second-order condition. The finite sample behavior is also examined and our methodology is applied to a real dataset.

Automated summary

In this paper, new asymptotic confidence intervals for extreme quantiles are proposed. These intervals are applicable when the underlying distribution is heavy-tailed and the quantiles are located outside the range of the available data. A novel approach based on the distribution of order statistics sampled from a uniform distribution is used instead of the traditional pivotal quantity-based approach. The convergence of coverage probability to the nominal value is established under a classical second-order condition. The methodology is also applied to a real dataset to examine its performance in finite sample settings.