Estimation of the marginal expected shortfall under asymptotic independence

@article{Cai2019EstimationOT,
  title={Estimation of the marginal expected shortfall under asymptotic independence},
  author={Juan-Juan Cai and Eni Musta},
  journal={Scandinavian Journal of Statistics},
  year={2019},
  volume={47},
  pages={56 - 83}
}
  • J. Cai, Eni Musta
  • Published 13 September 2017
  • Mathematics
  • Scandinavian Journal of Statistics
We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positively associated, which is modeled by the so‐called tail dependent coefficient. We construct an estimator of the marginal expected shortfall, which is shown to be asymptotically normal. The finite sample performance of the estimator is investigated in a small simulation study. The method is also applied to estimate the expected amount of rainfall at a weather… 

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In the context of bivariate random variables (Y^{(1)},Y^{(2)}), the marginal expected shortfall, defined as \mathbb E(Y^{(1)}|Y^{(2)} \ge Q_2(1-p)) for p small, where Q_2 denotes the quantile

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