Afrika Statistika

Robust estimator of distortion risk premiums for heavy-tailed losses

Brahim BRAHIMI and Kenioua ZOUBIR

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Abstract

We use the so-called t-Hill tail index estimator proposed by Fabián (2001), rather than Hill's one, to derive a robust estimator for the distortion risk premium of losses. Under the second-order condition of regular variation, we establish its asymptotic normality. By simulation study, we show that this new estimator is more robust than of Necir and Meraghni (2009) both for small and large samples.

Résumé

Nous utilisons l'estimateur de l'indice de queue dit t-Hill proposé par Fabián (2001), au lieu de l'estimateur de Hill, pour obtenir un estimateur robuste pour la prime de risque de distorsion des pertes. Sous la condition de second ordre de variation régulière, nous établissons sa normalité asymptotique. Par l'étude de simulation, nous montrons que ce nouvel estimateur est plus robuste que de celui proposé par Necir and Meraghni (2009) pour les petites et les grandes tailles d'échantillon.

Article information

Source
Afr. Stat., Volume 11, Number 1 (2016), 869-882.

Dates
First available in Project Euclid: 22 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.as/1461355420

Digital Object Identifier
doi:10.16929/as/2016.869.80

Mathematical Reviews number (MathSciNet)
MR3491568

Zentralblatt MATH identifier
1337.62089

Subjects
Primary: 62G10: Hypothesis testing 62G32: Statistics of extreme values; tail inference

Keywords
Distortion risk premiums Extreme values Tail Robustness

Citation

BRAHIMI, Brahim; ZOUBIR, Kenioua. Robust estimator of distortion risk premiums for heavy-tailed losses. Afr. Stat. 11 (2016), no. 1, 869--882. doi:10.16929/as/2016.869.80. https://projecteuclid.org/euclid.as/1461355420


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