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Confidence intervals for extreme Pareto-type quantiles |
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| Authors: | Sven Buitendag Jan Beirlant Tertius de Wet |
| Affiliation: | 1. Department of Mathematics, KU Leuven, Leuven, Belgium;2. Department of Mathematics, KU Leuven, Leuven, Belgium Department of Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa;3. Department of Statistics and Actuarial Science, Stellenbosch University, Stellenbosch, South Africa |
| 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. |
| Keywords: | confidence interval extreme value theory least squares quantiles ridge regression saddle-point approximation |