Bias-reduced estimation of Wang’s two-sided deviation risk measure under Lévy-stable regime. (English) Zbl 1258.91096

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

Afr. Stat. 7, No. 1, 441-458 (2012).

Summary: 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 D. Li et al. [J. Stat. Plann. Inference 140, No. 9, 2433–2441 (2010; Zbl 1188.62166)]. A simulation study is carried out to compare, in terms of bias and mean squared error, the new estimator with that introduced recently by A. Necir and D. Meraghni [J. Probab. Stat. 2010, Article ID 707146, 34 p. (2010; Zbl 1200.62050)].

MSC:

91B30	Risk theory, insurance (MSC2010)
62G32	Statistics of extreme values; tail inference
62G30	Order statistics; empirical distribution functions
62G05	Nonparametric estimation

Keywords:

bias reduction; high quantiles; Hill estimator; Lévy-stable distributions; L-statistics; order statistics; risk measure; second order regular variation; tail index

Citations:

Zbl 1188.62166; Zbl 1200.62050