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Nonparametric asymptotic confidence intervals for extreme quantiles
Author(s) -
Gardes Laurent,
Maistre Samuel
Publication year - 2023
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12610
Subject(s) - quantile , mathematics , cdf based nonparametric confidence interval , confidence interval , nonparametric statistics , statistics , order statistic , robust confidence intervals , range (aeronautics) , extreme value theory , coverage probability , econometrics , materials science , composite material
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.