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Estimation of the conditional tail moment for Weibull‐type distributions

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  • Yuri Goegebeur
  • Armelle Guillou
  • Jing Qin

Abstract

We consider the estimation of the conditional tail moment at extreme levels for the class of Weibull‐type distributions. A two‐step procedure is introduced where in the first stage one estimates the conditional tail moment at an intermediate level, followed by an extrapolation in the second stage. The asymptotic properties of the estimators introduced in the two stages are derived under suitable assumptions. The finite sample properties of the proposed estimator are examined with a simulation experiment. We conclude with two applications on real life data: wind speed measurements collected at an offshore wind farm and PM2.5 air pollution data.

Suggested Citation

  • Yuri Goegebeur & Armelle Guillou & Jing Qin, 2024. "Estimation of the conditional tail moment for Weibull‐type distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(4), pages 1782-1815, December.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:4:p:1782-1815
    DOI: 10.1111/sjos.12731
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    References listed on IDEAS

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    1. Juan-Juan Cai & John H. J. Einmahl & Laurens Haan & Chen Zhou, 2015. "Estimation of the marginal expected shortfall: the mean when a related variable is extreme," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 417-442, March.
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    6. Einmahl, J.H.J. & de Haan, L.F.M. & Li, D., 2006. "Weighted approximations of tail copula processes with applications to testing the bivariate extreme value condition," Other publications TiSEM 18b65ac3-ba79-4bff-ad53-2, Tilburg University, School of Economics and Management.
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