Asymptotic confidence intervals for extreme quantiles in a maximum domain of attraction
Résumé
Extreme quantiles are commonly used to assess the risk of extreme events such as large floods, extreme temperature, financial crisis among many others. When the underlying distribution belongs to a maximum domain of attraction, extreme quantile estimation has been widely studied in the literature but, surprisingly, little work has been dedicated to the construction of an asymptotic confidence interval. This is precisely the question addressed in this paper where a confidence interval for extreme quantile is proposed. This confidence interval can be used whatever the maximum domain of attraction of the distribution. The convergence of its coverage probability to the nominal one is established and its finite sample performance is investigated through a simulation study. An application on lifespan of French supercentenarians is done.
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