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Weighted estimate of extreme quantile: an application to the estimation of high flood return periods

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Abstract

Parametric models are commonly used in frequency analysis of extreme hydrological events. To estimate extreme quantiles associated to high return periods, these models are not always appropriate. Therefore, estimators based on extreme value theory (EVT) are proposed in the literature. The Weissman estimator is one of the popular EVT-based semi-parametric estimators of extreme quantiles. In the present paper we propose a new family of EVT-based semi-parametric estimators of extreme quantiles. To built this new family of estimators, the basic idea consists in assigning the weights to the k observations being used. Numerical experiments on simulated data are performed and a case study is presented. Results show that the proposed estimators are smooth, stable, less sensitive, and less biased than Weissman estimator.

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Acknowledgments

Financial support for this study was graciously provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Canada Research Chair Program. The authors wish to express their appreciation to the reviewers and the Editor-in-Chef for their invaluable comments and suggestions.

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Authors and Affiliations

  1. Canada Research Chair on the Estimation of Hydro-meteorological Variables, INRS-ETE, 490 rue de la Couronne, Quebec, QC, G1K 9A9, Canada

    Alexandre Lekina, Fateh Chebana & Taha B. M. J. Ouarda

  2. Service de l’enseignement des méthodes quantitatives de gestion, HEC Montréal, 3000 Chemin de la Côte-Sainte-Catherine, Montreal, QC, H3T 2A7, Canada

    Alexandre Lekina

  3. Institute Center for Water and Environment (iWATER), Masdar Institute of Science and Technology, P.O. Box 54224, Abu Dhabi, UAE

    Taha B. M. J. Ouarda

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  1. Alexandre Lekina
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  2. Fateh Chebana
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Correspondence to Alexandre Lekina.

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Lekina, A., Chebana, F. & Ouarda, T.B.M.J. Weighted estimate of extreme quantile: an application to the estimation of high flood return periods. Stoch Environ Res Risk Assess 28, 147–165 (2014). https://doi.org/10.1007/s00477-013-0705-2

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