Afr. Stat. 7 (1), 441-458, (November 2012)
Brahim Brahimi, Djamel Meraghni, Abdelhakim Necir, Sonia Touba
KEYWORDS: bias reduction, high quantiles, Hill estimator, Lévy-stable distributions, L-statistics, order statistics, risk measure, second order regular variation, tail index, 91B30, 62G32, 62G30, 62G05
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.