Robust estimator of distortion risk premiums for heavy-tailed losses

We use the so-called t-Hill tail index estimator proposed by Fabi\'an(2001), rather than Hill's one, to derive a robust estimator for the distortion risk premium of loss. 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.Comment: submitte

Distortion risk measures for sums of dependent losses

We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the sum and the dependence structure of risks, represented by copulas. Our goal is to propose risk measures that take into account the fluctuations of losses and possible correlations between risk components.Comment: Accepted 25 October 2010, Journal Afrika Statistika Vol. 5, N9, 2010, page 260--26

A Bias-reduced Estimator for the Mean of a Heavy-tailed Distribution with an Infinite Second Moment

We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked, in a simulation study, by four of the most popular goodness-of-fit tests for different sample sizes. Moreover, we compare, in terms of bias and mean squared error, our estimator with Peng's estimator (Peng, 2001) and we evaluate the accuracy of some resulting confidence intervals.Comment: Submitte

A semi-parametric estimation of copula models based on moments method under right censoring

Based on the classical estimation method of moments, a new copula estimator was proposed for censored bivariate data. As theoretical results, general formulas were proved with analytical forms of the obtained estimators. Taking into account Lopez and Saint-Pierre’s(2012)[19], Gribkova and Lopez’s (2015)[10] results, the asymptotic normality of the empirical survival copula was established. The dependence structure between the bivariate survival times was modeled under the assumption that the underlying copula is Archimedean. Accounting for various censoring patterns (singly or doubly censored), a simulation study was performed enlighten the behavior of the procedure estimation method, shown the efficiency and robustness of the new estimator proposed.Publisher's Versio

ASYMPTOTIC DISTRIBUTIONS OF LINEAR AND N

The limit distributions of linear and non-linear combinations of the kn = o(n) order statistics of i.i.d. random variables whosemaximum belongs to the domain of attraction of the Gumbel law are obtained. Our results may be applied in actuarial studies,estimation of scale-location parameters, estimation of squared deviation in tail of a distribution, robustness theory anddetection of the outliers in statistical data. It is also closely related to the moment estimator of Dekkers-Einmahl-de Hann(1989) for the index of an extreme distribution. This study completes that of Necir (1990, 1991a, 1991b, 2000a, 2000b)