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Dependent conditional tail expectation for extreme levels

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  • Goegebeur, Yuri
  • Guillou, Armelle
  • Qin, Jing

Abstract

We consider the estimation of the dependent conditional tail expectation, defined for a random vector (X,Y) with X≥0 as E(X|X>QX(1−p),Y>QY(1−p)), when E(X)<∞, and where QX and QY denote the quantile functions of X and Y, respectively. The distribution of X is assumed to be of Pareto-type while the distribution of Y is kept general. Using extreme-value arguments we introduce an estimator for this risk measure for the situation p≤1/n, where n is the number of available observations, i.e., focus is on estimation with extrapolation. The convergence in distribution of our estimator is established and its finite sample performance is illustrated on a simulation study. The method is then applied on wind gusts data set.

Suggested Citation

  • Goegebeur, Yuri & Guillou, Armelle & Qin, Jing, 2024. "Dependent conditional tail expectation for extreme levels," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:spapps:v:171:y:2024:i:c:s030441492400036x
    DOI: 10.1016/j.spa.2024.104330
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    References listed on IDEAS

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