Tail aligned composite quantile estimator for bootstrapping of high quantiles

Abstract

Abstract Reliable assessment of high quantiles, namely quantile with relatively low exceedance probability, based on available sample is of interest in hydrology, meteorology, finance and many other fields. Interval estimation of extreme quantities in real-world mechanisms is essential, but it is challenging due to complexities in underlying data-generating processes, small sample sizes, data are not normal, failure of the standard statistical assumptions etc. leading to huge stochastic uncertainties. A composite quantile function estimator aligned using tail of generalized extreme value distribution is employed to construct bootstrap confidence intervals for high-order quantiles. The proposed semi-parametric estimator is shown to be asymptotically unbiased and consistent. The utility of the proposed estimator in comparison with traditional nonparametric and parametric bootstrap in terms of coverage probability for small size and case study application to real-world precipitation datasets has been illustrated. Limitations posed in computations and scope for future work is highlighted.