Tarik Bahraoui | Université du Québec à Trois-Rivières (original) (raw)

Papers by Tarik Bahraoui

Journal of Multivariate Analysis, Aug 1, 2014

The selection of a copula that appropriately describes the dependence structure of a bivariate di... more The selection of a copula that appropriately describes the dependence structure of a bivariate distribution function is an issue of a prime interest in multivariate statistical analysis. The most popular methods of testing are those based on the empirical copula and on Kendall's process; these tests require the use of the parametric bootstrap, which is computationally heavy. This paper introduces the concept of C-power functions associated to bivariate copulas. In the first step, their theoretical properties are explored and computations for many popular dependence models are provided. Then, empirical counterparts of these functions are proposed and the weak convergence of suitably normalized versions is obtained from an application of the functional delta method. In addition, a multiplier bootstrap method for these C-power processes is described and validated. While of an independent interest to treat many hypotheses related to copulas, these newly introduced tools are used to develop a goodness-of-fit test for bivariate multi-parameter copula models. The recursive nature of the C-power functions induces easily computable formulas for the test statistics and suggests a sequential method of testing. The sample properties of this goodness-of-fit test are investigated and compared to those of competing procedures, and its usefulness is illustrated on some pairs of the multivariate Uranium exploration data set.

Scandinavian Journal of Statistics, Oct 18, 2021

Journal of Multivariate Analysis, 2022

Au terme de ce t ravail de maîtrise, je t iens à exprimer ma profond e grat itude et mes remercie... more Au terme de ce t ravail de maîtrise, je t iens à exprimer ma profond e grat itude et mes remerciements sincères à M. Jean-François Quessy, qui est mon directeur de recherche et professeur de statistique au département de Mathématiques et d 'information de l'Université du Québec à Trois-Rivières (UQTR). Je lui suis reconnaissant du temps qu'il m'a consacré, de ses direct ives précieuses et de la qualité de son encadrement durant ces deux années. J 'adresse également des remerciements aux professeurs Mhamed Mesfioui et Fathallah Nouboud, du département de Mathématiques et d 'information de l'UQTR. Leur appui moral et leurs encouragements durant ces deux années d 'étude à l'UQTR ont été t rès appréciés. Je veux aussi remercier les membres du jury, MM. Taoufik Bouezmarni et Mhamed Mesfioui, pour avoir accepté de lire et évaluer mon mémoire. Leurs judicieux commentaires m 'ont permis d'améliorer la version finale de ce t ravail. Mes études de maîtrise ont ét é financées par des subventions de recherche octroyées à M. Jean-François Quessy par le Fo nds Québécois de Recherche Nature et Technologies et par le Conseil National de Recherche en Sciences Naturelles et en Génie du Canada. Je remercie aussi l'Institut des Sciences Math ématiques du Québec pour les bourses d'étude qu 'ils m 'ont accordées. Enfin , la vie continue. A la memoria de mi padre TABLE DES MATIÈRES 5.5.1 Efficiency of the parameter estimation .. 5.5.2 Efficiency of t he goodness-of-fit procedures 5.6 Illustration on t he Uranium exploration data set Chapitre 6. Conclusion Références Annexe A. Estimation du générateur Archimédien A.1 Un estimateur plug-in ...

Canadian journal of statistics, Oct 4, 2013

Statistical tools to check whether the underlying copula of a pair of random variables is symmetr... more Statistical tools to check whether the underlying copula of a pair of random variables is symmetric are developed. The proposed methods are based on the theoretical and empirical versions of the C-power functions introduced and formally studied by Bahraoui & Quessy (2013). On one part, a methodology is developed for testing the null hypothesis that the copula of a given population is symmetric. To this end, a sequential testing procedure is proposed where at each level, the P-value is estimated with the help of the multiplier bootstrap method. On another side, a related graphical method is proposed in order to gain an idea of the degree of asymmetry in bivariate data. The good properties of the methods in small samples are investigated with the help of Monte Carlo simulations under various scenarios of symmetric and asymmetric dependence. The newly introduced procedures are used to analyse the Nutrient and the Walker Lake data sets.

Scandinavian Journal of Statistics, 2017

A general class of rank statistics based on the characteristic function is introduced for testing... more A general class of rank statistics based on the characteristic function is introduced for testing goodness-of-fit hypotheses about the copula of a continuous random vector. These statistics are defined as L 2 weighted functional distances between a nonparametric estimator and a semi-parametric estimator of the characteristic function associated with a copula. It is shown that these statistics behave asymptotically as degenerate V-statistics of order four and that the limit distributions have representations in terms of weighted sums of independent chi-square variables. The consistency of the tests against general alternatives is established and an asymptotically valid parametric bootstrap is suggested for the computation of the critical values of the tests. The behaviour of the new tests in small and moderate sample sizes is investigated with the help of simulations and compared with a competing test based on the empirical copula. Finally, the methodology is illustrated on a five-dimensional data set.

Canadian Journal of Statistics, 2013

ABSTRACT Statistical tools to check whether the underlying copula of a pair of random variables i... more ABSTRACT Statistical tools to check whether the underlying copula of a pair of random variables is symmetric are developed. The proposed methods are based on the theoretical and empirical versions of the C-power functions introduced and formally studied by Bahraoui & Quessy (2013). On one part, a methodology is developed for testing the null hypothesis that the copula of a given population is symmetric. To this end, a sequential testing procedure is proposed where at each level, the P-value is estimated with the help of the multiplier bootstrap method. On another side, a related graphical method is proposed in order to gain an idea of the degree of asymmetry in bivariate data. The good properties of the methods in small samples are investigated with the help of Monte Carlo simulations under various scenarios of symmetric and asymmetric dependence. The newly introduced procedures are used to analyse the Nutrient and the Walker Lake data sets. The Canadian Journal of Statistics 41: 637-656; 2013 (c) 2013 Statistical Society of Canada

Electronic Journal of Statistics, 2017

Journal of Multivariate Analysis

Scandinavian Journal of Statistics

Dependence Modeling, Dec 1, 2018

This paper proposes competing procedures to the tests of symmetry for bivariate copulas of Genest... more This paper proposes competing procedures to the tests of symmetry for bivariate copulas of Genest, Nešlehová and Quessy (2012). To this end, the null hypothesis of symmetry is expressed in terms of the copula characteristic function that uniquely determines the copula of a given bivariate population with continuous marginal distributions. Then, test statistics based on L weighted distances computed from an empirical version of the copula characteristic function are proposed. Their asymptotic behavior is derived under the null hypothesis as well as under general alternatives. In particular, it is established that these rank statistics behave asymptotically as rst-order degenerate V-statistics under the null hypothesis and this large-sample representation is exploited in order to provide suitably adapted multiplier bootstrap versions for the computation of p-values. The simulations that are reported show that the new tests are more powerful than the competing methods based on the empirical copula introduced by Genest, Nešlehová and Quessy (2012).

Journal of Multivariate Analysis, 2014