Afrika Statistika

Bias-reduced estimation of Wang's two-sided deviation risk measure under Lévy-stable regime

Brahim Brahimi, Djamel Meraghni, Abdelhakim Necir, and Sonia Touba

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Abstract

Several risk measures, such as the distorted insurance premium and the two-sided deviation (TSD) measure, can be regarded as L-functionals with specific weight functions. In this paper, we focus on the TSD risk measure as we define a new estimator by using the bias-reduced estimators of extreme quantiles proposed by Li et al. 2010. A simulation study is carried out to compare, in terms of bias and mean squared error, the new estimator with that introduced recently by Necir and Meraghni 2010.

Article information

Source
Afr. Stat., Volume 7, Number 1 (2012), 441-458.

Dates
First available in Project Euclid: 1 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.as/1359744268

Mathematical Reviews number (MathSciNet)
MR3034389

Zentralblatt MATH identifier
1258.91096

Subjects
Primary: 91B30: Risk theory, insurance 62G32: Statistics of extreme values; tail inference
Secondary: 62G30: Order statistics; empirical distribution functions 62G05: Estimation

Keywords
Bias reduction High quantiles Hill estimator Lévy-stable distributions L-statistics Order statistics Risk Measure Second order regular variation Tail index

Citation

Brahimi, Brahim; Meraghni, Djamel; Necir, Abdelhakim; Touba, Sonia. Bias-reduced estimation of Wang's two-sided deviation risk measure under Lévy-stable regime. Afr. Stat. 7 (2012), no. 1, 441--458. https://projecteuclid.org/euclid.as/1359744268


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