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Abdelhakim Necir

Publications and source records attributed to Abdelhakim Necir.

24 records · Page 2Linked to original sources
arXiv2012

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.

stat.ME↗
arXiv2012

A semiparametric estimation of copula models based on the method of moments

Using the classical estimation method of moments, we propose a new semiparametric estimation procedure for multi-parameter copula models. Consistency and asymptotic normality of the obtained estimators are established. By considering an Archimedean copula model, an extensive simulation study, comparing these estimators with the pseudo maximum likelihood, rho-inversion and tau-inversion ones, is carried out. We show that, with regards to the other methods, the moment based estimation is quick and simple to use with reasonable bias and root mean squared error.

stat.ME↗
arXiv2011

Copula representation of bivariate L-moments : A new estimation method for multiparameter 2-dimentional copula models

Recently, Serfling and Xiao (2007) extended the L-moment theory (Hosking, 1990) to the multivariate setting. In the present paper, we focus on the two-dimension random vectors to establish a link between the bivariate L-moments (BLM) and the underlying bivariate copula functions. This connection provides a new estimate of dependence parameters of bivariate statistical data. Consistency and asymptotic normality of the proposed estimator are established. Extensive simulation study is carried out to compare estimators based on the BLM, the maximum likelihood, the minimum distance and rank approximate Z-estimation. The obtained results show that, when the sample size increases, BLM-based estimation performs better as far as the bias and computation time are concerned. Moreover, the root mean squared error (RMSE) is quite reasonable and less sensitive in general to outliers than those of the above cited methods. Further, we expect that the BLM method is an easy-to-use tool for the estimation of multiparameter copula models.

stat.ME↗
arXiv2011

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.

stat.ME↗
arXiv2011

Coupled risk measures and their empirical estimation when losses follow heavy-tailed distributions

Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a number of risk measures that are of the form of ratios, or even more complex combinations, of two L-functionals. In the present paper we call such combinations `coupled risk measures' and develop a statistical inferential theory for them when losses follow heavy-tailed distributions. Our theory implies -at a stroke- statistical inferential results for absolute and relative distortion risk measures, weighted premium calculation principles, as well as for many indices of economic inequality that have appeared in the econometric literature.

math.ST↗