Abdelhakim Necir

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In this paper we study some asymptotic properties of the kernel conditional quantile estimator with randomly left-truncated data which exhibit some kind of dependence. We extend the result obtained by Lemdani, Ould-Sa¨ıd and Poulin [16] in the iid case. The uniform strong convergence rate of the estimator under strong mixing hypothesis is obtained.
The conditional tail expectation CTE is an important actuarial risk measure and a useful tool in financial risk assessment. Under the classical assumption that the second moment of the loss variable is finite, the asymptotic normality of the nonparametric CTE estimator has already been established in the literature. The noted result, however, is not(More)
By transforming a data set with a modification of the Champernowne distribution function, a kernel quantile estimator for heavy-tailed distributions is given. The asymptotic mean squared error (AMSE) of the proposed estimator and related asymptotically optimal bandwidth are evaluated. Some simulations are drawn to show the performance of the obtained(More)
We introduce a consistent estimator of the extreme value index under random truncation based on a single sample fraction of top observations from truncated and truncation data. We establish the asymptotic normality of the proposed estimator by making use of the weighted tail-copula process framework and we check its finite sample behavior through some(More)
Résumé. Dans les années 60, les travaux de Mandelbrot sur les fluctuations boursières montrèrent que le modèle gaussien ne convenait pas pour décrire les rendements d’actifs. Mandelbrot (1963) puis Fama (1965) proposèrent la distribution Lévy-stable, dont les propriétés sont très proches de celles des distributions empiriques à queues lourdes, comme(More)
Making use of the peaks over threshold POT estimation method, we propose a semiparametric estimator for the renewal function of interoccurrence times of heavy-tailed insurance claims with infinite variance. We prove that the proposed estimator is consistent and asymptotically normal, and we carry out a simulation study to compare its finite-sample behavior(More)
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