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Asymptotic behavior of the extrapolation error associated with the estimation of extreme quantiles

Authors
  • Albert, Clément
  • Dutfoy, Anne
  • Girard, Stéphane
Publication Date
Feb 26, 2018
Source
Kaleidoscope Open Archive
Keywords
Language
English
License
Unknown
External links

Abstract

We investigate the asymptotic behavior of the (relative) extrapolation error associated with some estimators of extreme quantiles based on extreme-value theory. It is shown that the extrapolation error can be interpreted as the remainder of a first order Taylor expansion. Necessary and sufficient conditions are then provided such that this error tends to zero as the sample size increases. Interestingly, in case of the so-called Exponential Tail estimator, these conditions lead to a subdivision of Gumbel maximum domain of attraction into three subsets. In constrast, the extrapolation error associated with Weissman estimator has a common behavior over the whole Fréchet maximum domain of attraction. First order equivalents of the extrapolation error are then derived and their accuracy is illustrated numerically.

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