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Large Quantile Estimation in a Multivariate Setting

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  • Dehaan, L.
  • Huang, X.

Abstract

An asymptotic theory is developed for the estimation of high quantile curves, i.e., sets of points in higher dimensional space for which the exeedance probability is pn, with npn --> 0 (n --> [infinity]). Here n is the number of available observations. This is the situation of interest if one wants to protect against a calamity that has not yet occurred. Asymptotic normality of the estimated quantile curve is proved under appropriate conditions, including the domain of the attraction condition for multivariate extremes.

Suggested Citation

  • Dehaan, L. & Huang, X., 1995. "Large Quantile Estimation in a Multivariate Setting," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 247-263, May.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:2:p:247-263
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    Cited by:

    1. Elena Di Bernardino & Didier Rullière, 2012. "Distortions of multivariate risk measures: a level-sets based approach," Working Papers hal-00756387, HAL.
    2. Di Bernardino, Elena & Rullière, Didier, 2013. "Distortions of multivariate distribution functions and associated level curves: Applications in multivariate risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 190-205.
    3. Einmahl, J.H.J. & Li, J. & Liu, R.Y., 2006. "Extreme Value Theory Approach to Simultaneous Monitoring and Thresholding of Multiple Risk Indicators," Discussion Paper 2006-104, Tilburg University, Center for Economic Research.
    4. Elena Bernardino & Thomas Laloë & Rémi Servien, 2015. "Estimating covariate functions associated to multivariate risks: a level set approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 497-526, July.
    5. Einmahl, J.H.J. & de Haan, L.F.M. & Krajina, A., 2009. "Estimating Extreme Bivariate Quantile Regions," Discussion Paper 2009-29, Tilburg University, Center for Economic Research.
    6. Elena Di Bernardino & Clémentine Prieur, 2014. "Estimation of multivariate conditional-tail-expectation using Kendall's process," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 241-267, June.
    7. Barme-Delcroix, Marie-Francoise & Gather, Ursula, 2007. "Limit laws for multidimensional extremes," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1750-1755, December.
    8. Elena Di Bernardino & Thomas Laloë & Véronique Maume-Deschamps & Clémentine Prieur, 2013. "Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory," Post-Print hal-00580624, HAL.
    9. repec:hal:wpaper:hal-00750873 is not listed on IDEAS

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