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Large Quantile Estimation in a Multivariate Setting

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  • Dehaan, L.
  • Huang, X.
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 53 (1995)
    Issue (Month): 2 (May)
    Pages: 247-263

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    Handle: RePEc:eee:jmvana:v:53:y:1995:i:2:p:247-263

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    Cited by:
    1. 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.
    2. Elena Di Bernardino & Didier Rullière, 2012. "Distortions of multivariate risk measures: a level-sets based approach," Working Papers hal-00756387, HAL.
    3. Einmahl, J.H.J. & Haan, L.F.M. de & Krajina, A., 2009. "Estimating Extreme Bivariate Quantile Regions," Discussion Paper 2009-29, Tilburg University, Center for Economic Research.
    4. Elena Di Bernardino & Didier Rullière, 2013. "Distortions of multivariate distribution functions and associated level curves: applications in multivariate risk theory," Post-Print hal-00750873, HAL.
    5. 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.
    6. repec:hal:wpaper:hal-00750873 is not listed on IDEAS
    7. Barme-Delcroix, Marie-Francoise & Gather, Ursula, 2007. "Limit laws for multidimensional extremes," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1750-1755, December.

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