Papers by Laurence Reboul
HAL (Le Centre pour la Communication Scientifique Directe), 2015
Population aging challenges the fiscal balances of a state, the role of the elderly and young peo... more Population aging challenges the fiscal balances of a state, the role of the elderly and young people in society, the renewal of the labor market, resource allocation, etc. Populations age at different rates so that some regions are catching up with others, while others continue to widen the gap. The concept of convergence can be applied to demographic indicators, including aging. This paper aims to study the spatial dimension of the convergence of population aging. We decided to use Markov chains to analyse the spatial convergence of southern Europe (Portugal, Spain, France, Italy) from 1998 to 2013.
HAL (Le Centre pour la Communication Scientifique Directe), Oct 21, 2021
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
HAL (Le Centre pour la Communication Scientifique Directe), 2011
In this paper we propose a smooth test of comparison of two distribution functions. This test ada... more In this paper we propose a smooth test of comparison of two distribution functions. This test adapts to the classical two-sample problem as well as that of paired populations, including discrete distributions. A simulation study and an application to real data show its good performances.
ABSTRACT In large networks, the detection of vertex subsets more densely connected than others, c... more ABSTRACT In large networks, the detection of vertex subsets more densely connected than others, called communities, is a problem encountered in several disciplines - biology (interaction ks between proteins), computer science (information search on the Web), but also operational research and sociology (groups in social networks). These communities play an important role in the structural organization of networks. Actually, this question consists in identifying clusters in graphs. This problem is therefore closely related to graph partitioning, with the following characteristic: depending on what is expected with these communities, the clusters may or not be disjoint. In biology, protein-protein interaction networks have to be analyzed, in order to predict protein cellular functions. Since many proteins can share several functions, it is appropriate to attempt to build a covering set of classes rather a partition, that is a system of overlapping clusters. The same happens for social networks in which the individuals may belong to several groups. Traditional clustering methods can be used; namely, methods of graph partitioning maximizing some criterion. Among numerous criteria evaluating the quality of a partition, we only refer here to the concept of modularity introduced by Girwan and Newman (2004). Unfortunately, modularity optimization over graph vertices partitions is a NP-hard problem. Consequently, it is the same for graph coverings. We must therefore use heuristic methods when the studied graphs get large. In this chapter, we propose two new approximation methods, the first one for partitions, the other one for coverings, tending to optimize the modularity criterion. These methods are based on a process starting from an initial overlapping class system and converging towards another class system. For strict partitions, a fusion-fission method of clusters, from the edge set is carried out until the current clusters are no longer overlapping; for coverings, only the fusion part is applied, but from several starting sets. An efficiency study, in which our methods and their variants are compared to other algorithms on simulated graphs, attests their suitability.
Annals of Statistics, Jun 1, 2005
This paper deals with a nonparametric shape respecting estimation method for U-shaped or unimodal... more This paper deals with a nonparametric shape respecting estimation method for U-shaped or unimodal functions. A general upper bound for the nonasymptotic L 1-risk of the estimator is given. The method is applied to the shape respecting estimation of several classical functions, among them typical intensity functions encountered in the reliability field. In each case, we derive from our upper bound the spatially adaptive property of our estimator with respect to the L 1-metric: it approximately behaves as the best variable binwidth histogram of the function under estimation.
Statistical Inference for Stochastic Processes
In this paper we propose to generalize the recent works of [4] and [3] on the comparison of the m... more In this paper we propose to generalize the recent works of [4] and [3] on the comparison of the marginal distributions of two strictly stationary processes. Our aim is to test the equality the whole distributions of two such processes. For that task, we compare all possible d dimensional joint distributions of both processes. Our procedure consist in expanding their densities in a multivariate orthogonal basis and comparing their k rst coecients. The number d of dimensions to consider and the number k of coecients to compare in view to perform the test can growth with the sample size and are automatically selected by a two step data driven procedure. The method works for possibly paired, short or long range dependent processes. A simulation study shows the good behavior of the test procedure. In particular we apply our method to compare ARFIMA processes. Real data sets also illustrate this approach.
HAL (Le Centre pour la Communication Scientifique Directe), Oct 21, 2021
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Le vieillissement demographique constitue un phenomene a enjeu social. Il remet en cause les equi... more Le vieillissement demographique constitue un phenomene a enjeu social. Il remet en cause les equilibres budgetaires d’un Etat, les solidarites familiales, la place des personnes âgees et des jeunes dans la societe, le renouvellement du marche de l’emploi, l’allocation des ressources etc. Les populations ne vieillissent pas toutes a la meme vitesse. Ainsi, des territoires en rattrapent d’autres, ou se font distancer par d’autres. S’il a ete initialement developpe en economie, le concept de convergence peut legitimement s’appliquer aux indicateurs demographiques, dont le vieillissement fait partie. Cette presentation se propose d’etudier la dimension spatiale du phenomene de convergence du vieillissement demographique. Parmi les methodes disponibles, nous utilisons les chaines de Markov pour analyser ce que nous appelons la convergence spatiale. Nous choisissons l’Europe meridionale (Portugal, Espagne, France, Italie) comme aire d’etude, et la periode temporelle choisie est 1998-2013.
Statistique Et Enseignement, Sep 7, 2012
Dans un souci de transversalité entre les enseignements de statistique et d'informatique dispensé... more Dans un souci de transversalité entre les enseignements de statistique et d'informatique dispensés dans nos formations, nous avons élaboré un logiciel pour la préparation et les analyses de base d'un corpus textuel. Cet outil permet d'accompagner nos étudiants dans leur mise en application de leurs connaissances à la fois en analyse statistique textuelle et en gestion de bases de données.
Http Www Theses Fr, 1998
Cette these comporte deux parties distinctes relatives a la mise en oeuvre et a la validation de ... more Cette these comporte deux parties distinctes relatives a la mise en oeuvre et a la validation de modeles statistiques utilises en fiabilite. Dans un premier temps, nous proposons une methode d'estimation non parametrique sous restriction de forme : il s'agit d'estimer des fonctions unimodales (resp. Admettant une courbe en forme de u). Etant donnee une fonction g inconnue de primitive g et un estimateur en escalier $$g de g, l'estimateur $$g de g est defini comme la derivee de la fonction convexe puis concave (resp. Concave puis convexe) la mieux ajustee a $$g. Notre estimateur est construit a partir des donnees a l'aide d'un algorithme simple. Nous etablissons un controle de son risque non-asymptotique en norme l#1, qui permet de relier ses proprietes a celles de $$z = $$g g. Sous des hypotheses convenables sur $$z, nous montrons que $$g se comporte approximativement comme le meilleur histogramme de g. L'adaptativite et la simplicite de construction de notre estimateur lui conferent une superiorite sur les methodes classiques d'estimation par histogramme ou par noyau avec parametre fixe, en l'absence d'hypothese de regularite sur g ou dans des cadres non-asymptotiques. Entre autres applications de ces resultats, nous etudions l'estimation du taux de panne avec et sans censure et de l'intensite d'un processus de poisson, fonctions pour lesquelles l'hypothese d'une courbe en u est souvent plus naturelle que des hypotheses de regularite. Dans la deuxieme partie de cette these, nous presentons des tests de validation de modeles parametriques de processus de poisson. Nous considerons des statistiques de type kolmogorov-smirnov dont nous etudions le comportement asymptotique sous l'hypothese d'adequation au modele teste. Nous en deduisons des formules d'approximation des quantiles de test, qui doivent etre validees numeriquement dans chaque cas particulier. Nous les etudions sur un modele classiquement utilise en fiabilite.
Bichot/Graph Partitioning, 2013
ABSTRACT In large networks, the detection of vertex subsets more densely connected than others, c... more ABSTRACT In large networks, the detection of vertex subsets more densely connected than others, called communities, is a problem encountered in several disciplines - biology (interaction ks between proteins), computer science (information search on the Web), but also operational research and sociology (groups in social networks). These communities play an important role in the structural organization of networks. Actually, this question consists in identifying clusters in graphs. This problem is therefore closely related to graph partitioning, with the following characteristic: depending on what is expected with these communities, the clusters may or not be disjoint. In biology, protein-protein interaction networks have to be analyzed, in order to predict protein cellular functions. Since many proteins can share several functions, it is appropriate to attempt to build a covering set of classes rather a partition, that is a system of overlapping clusters. The same happens for social networks in which the individuals may belong to several groups. Traditional clustering methods can be used; namely, methods of graph partitioning maximizing some criterion. Among numerous criteria evaluating the quality of a partition, we only refer here to the concept of modularity introduced by Girwan and Newman (2004). Unfortunately, modularity optimization over graph vertices partitions is a NP-hard problem. Consequently, it is the same for graph coverings. We must therefore use heuristic methods when the studied graphs get large. In this chapter, we propose two new approximation methods, the first one for partitions, the other one for coverings, tending to optimize the modularity criterion. These methods are based on a process starting from an initial overlapping class system and converging towards another class system. For strict partitions, a fusion-fission method of clusters, from the edge set is carried out until the current clusters are no longer overlapping; for coverings, only the fusion part is applied, but from several starting sets. An efficiency study, in which our methods and their variants are compared to other algorithms on simulated graphs, attests their suitability.
The Annals of Statistics, 2005
This paper deals with a nonparametric shape respecting estimation method for U-shaped or unimodal... more This paper deals with a nonparametric shape respecting estimation method for U-shaped or unimodal functions. A general upper bound for the nonasymptotic L 1-risk of the estimator is given. The method is applied to the shape respecting estimation of several classical functions, among them typical intensity functions encountered in the reliability field. In each case, we derive from our upper bound the spatially adaptive property of our estimator with respect to the L 1-metric: it approximately behaves as the best variable binwidth histogram of the function under estimation.
Le Centre pour la Communication Scientifique Directe - HAL - Université Paris 1 Panthéon-Sorbonne, 2015
International audienc
Statistical Inference for Stochastic Processes, 2022
In this paper we propose to generalize the recent works of [4] and [3] on the comparison of the m... more In this paper we propose to generalize the recent works of [4] and [3] on the comparison of the marginal distributions of two strictly stationary processes. Our aim is to test the equality the whole distributions of two such processes. For that task, we compare all possible d dimensional joint distributions of both processes. Our procedure consist in expanding their densities in a multivariate orthogonal basis and comparing their k rst coecients. The number d of dimensions to consider and the number k of coecients to compare in view to perform the test can growth with the sample size and are automatically selected by a two step data driven procedure. The method works for possibly paired, short or long range dependent processes. A simulation study shows the good behavior of the test procedure. In particular we apply our method to compare ARFIMA processes. Real data sets also illustrate this approach.
Annals of the Institute of Statistical Mathematics, 2019
In this paper, we adapt a data-driven smooth test to the comparison of the marginal distributions... more In this paper, we adapt a data-driven smooth test to the comparison of the marginal distributions of two independent, short or long memory, strictly stationary linear sequences. Some illustrations are shown to evaluate the performances of our test.
Journal of Multivariate Analysis, 2015
In this paper we propose a smooth test of comparison for the marginal distributions of two possib... more In this paper we propose a smooth test of comparison for the marginal distributions of two possibly dependent strictly stationary sequences. We first state a general test procedure. Several cases of dependence are then investigated, allowing to cover various real situations. The test is applied to both simulated data and real datasets obtained from financial markets.
Lithuanian Mathematical Journal, 2020
In this paper, we study some asymptotic properties of CFG estimator of the Pickands dependence fu... more In this paper, we study some asymptotic properties of CFG estimator of the Pickands dependence function of strictly stationary absolutely regular sequences of bivariate extremes. We then propose an asymptotic test of independence of the vector margins. Finite sample properties of the estimate are investigated by simulation. MSC: 62G32 Statistics of extreme values; tail inference 62G10 Nonparametric hypothesis testing 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62E20 Asymptotic distribution theory in statistics 60G10 Stationary stochastic processes
Population aging challenges the fiscal balances of a state, the role of the elderly and young peo... more Population aging challenges the fiscal balances of a state, the role of the elderly and young people in society, the renewal of the labor market, resource allocation, etc. Populations age at different rates so that some regions are catching up with others, while others continue to widen the gap. The concept of convergence can be applied to demographic indicators, including aging. This paper aims to study the spatial dimension of the convergence of population aging. We decided to use Markov chains to analyse the spatial convergence of southern Europe (Portugal, Spain, France, Italy) from 1998 to 2013.
Community detection, also known as graph partitioning, is a useful tool for analysing and underst... more Community detection, also known as graph partitioning, is a useful tool for analysing and understanding data taking the form of non-oriented, simple networks. In particular, detecting communities in protein-protein interaction networks (PPI) is impor- tant in functional prediction. Modularity is a well known criterion of quality of a graph partition. In this paper, we propose a new partitioning method based on the optimization of the modularity over the set of partitions of a network using a fusion-fission process. A simulation study shows that our method is competitive. It is used to find communities of proteins in the Drosophila PPI network.
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Papers by Laurence Reboul