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

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, Stephane 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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