Confidence intervals for extreme Pareto‐type quantiles. (25th June 2019)

• Record Type: Journal Article
• Authors: Buitendag, Sven; Beirlant, Jan; de Wet, Tertius
• Is Part Of: Scandinavian journal of statistics. Volume 47:Number 1(2020:Mar.)
• Page Start: 36
• Page End: 55
• Publication Date: 2019-06-25
• Subjects: confidence interval -- extreme value theory -- least squares -- quantiles -- ridge regression -- saddle‐point approximation; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12396
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: In this paper, we revisit the construction of confidence intervals for extreme quantiles of Pareto‐type distributions. A novel asymptotic pivotal quantity is proposed for these quantile estimators, which leads to new asymptotic confidence intervals that exhibit more accurate coverage probability. This pivotal quantity also allows for the construction of a saddle‐point approximation, from which a second set of new confidence intervals follows. The small‐sample properties and utility of these confidence intervals are studied using simulations and a case study from insurance.