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Reduced-bias estimator of the Conditional Tail Expectation of heavy-tailed distributions

El Hadji Deme 1, 2, 3 Stéphane Girard 3, 2, * Armelle Guillou 4
* Corresponding author
2 MISTIS [2007-2015] - Modelling and Inference of Complex and Structured Stochastic Systems [2007-2015]
Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019], LJK [2007-2015] - Laboratoire Jean Kuntzmann [2007-2015], Inria Grenoble - Rhône-Alpes
Abstract : Several risk measures have been proposed in the literature. In this paper, we focus on the estimation of the Conditional Tail Expectation (CTE). Its asymptotic normality has been first established in the literature under the classical assumption that the second moment of the loss variable is finite, this condition being very restrictive in practical applications. Such a result has been extended by Necir {\it et al.} (2010) in the case of infinite second moment. In this framework, we propose a reduced-bias estimator of the CTE. We illustrate the efficiency of our approach on a small simulation study and a real data analysis.
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El Hadji Deme, Stéphane Girard, Armelle Guillou. Reduced-bias estimator of the Conditional Tail Expectation of heavy-tailed distributions. M. Hallin et al. Mathematical Statistics and Limit Theorems, Springer, pp.105-123, 2015, ⟨10.1007/978-3-319-12442-1_7⟩. ⟨hal-00823260v2⟩

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