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Confidence intervals for extreme Pareto‐type quantiles

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  • Sven Buitendag
  • Jan Beirlant
  • Tertius de Wet

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.

Suggested Citation

  • Sven Buitendag & Jan Beirlant & Tertius de Wet, 2020. "Confidence intervals for extreme Pareto‐type quantiles," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(1), pages 36-55, March.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:1:p:36-55
    DOI: 10.1111/sjos.12396
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