The Experts below are selected from a list of 14277 Experts worldwide ranked by ideXlab platform
Miriam Isabel Seifert - One of the best experts on this subject based on the ideXlab platform.
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A conditional limit theorem for a bivariate representation of a univariate Random Variable and conditional extreme values
Extremes, 2016Co-Authors: Philippe Barbe, Miriam Isabel SeifertAbstract:We first consider a Real Random Variable X represented through a Random pair ( R , T ) and a deterministic function u as X = R ⋅ u ( T ). Under quite weak assumptions we prove a limit theorem for ( R , T ) given X > x , as x tends to infinity. The novelty of our paper is to show that this theorem for the representation of the univariate Random Variable X permits us to obtain in an elegant manner conditional limit theorems for Random pairs ( X , Y ) = R ⋅( u ( T ), v ( T )) given that X is large. Our approach allows to deduce new results as well as to recover under considerably weaker assumptions results obtained previously in the literature. Consequently, it provides a better understanding and systematization of limit statements for the conditional extreme value models.
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a conditional limit theorem for a bivariate representation of a univariate Random Variable and conditional extreme values
arXiv: Probability, 2013Co-Authors: Philippe Barbe, Miriam Isabel SeifertAbstract:We consider a Real Random Variable X represented through a Random pair of Real Random Variables (R,T) and a deterministic function u as X=Ru(T). Under some additional assumptions, we prove a limit theorem for (R,T) given X>x, as x tends to infinity. As a consequence, we derive conditional limit theorems for Random pairs (X,Y)=(Ru(T),Rv(T)) given that X is large. These results imply earlier ones which were obtained in the literature under stronger assumptions.
Philippe Barbe - One of the best experts on this subject based on the ideXlab platform.
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A conditional limit theorem for a bivariate representation of a univariate Random Variable and conditional extreme values
Extremes, 2016Co-Authors: Philippe Barbe, Miriam Isabel SeifertAbstract:We first consider a Real Random Variable X represented through a Random pair ( R , T ) and a deterministic function u as X = R ⋅ u ( T ). Under quite weak assumptions we prove a limit theorem for ( R , T ) given X > x , as x tends to infinity. The novelty of our paper is to show that this theorem for the representation of the univariate Random Variable X permits us to obtain in an elegant manner conditional limit theorems for Random pairs ( X , Y ) = R ⋅( u ( T ), v ( T )) given that X is large. Our approach allows to deduce new results as well as to recover under considerably weaker assumptions results obtained previously in the literature. Consequently, it provides a better understanding and systematization of limit statements for the conditional extreme value models.
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a conditional limit theorem for a bivariate representation of a univariate Random Variable and conditional extreme values
arXiv: Probability, 2013Co-Authors: Philippe Barbe, Miriam Isabel SeifertAbstract:We consider a Real Random Variable X represented through a Random pair of Real Random Variables (R,T) and a deterministic function u as X=Ru(T). Under some additional assumptions, we prove a limit theorem for (R,T) given X>x, as x tends to infinity. As a consequence, we derive conditional limit theorems for Random pairs (X,Y)=(Ru(T),Rv(T)) given that X is large. These results imply earlier ones which were obtained in the literature under stronger assumptions.
Rafael L Greenblatt - One of the best experts on this subject based on the ideXlab platform.
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singular behavior of the leading lyapunov exponent of a product of Random 2 times 2 matrices
Communications in Mathematical Physics, 2017Co-Authors: Giuseppe Genovese, Giambattista Giacomin, Rafael L GreenblattAbstract:We consider a certain infinite product of Random \({2 \times 2}\) matrices appearing in the solution of some 1 and 1 + 1 dimensional disordered models in statistical mechanics, which depends on a parameter \({\varepsilon > 0}\) and on a Real Random Variable with distribution \({\mu}\). For a large class of \({\mu}\), we prove the prediction by Derrida and Hilhorst (J Phys A 16:2641, 1983) that the Lyapunov exponent behaves like \({C \epsilon^{2 \alpha}}\) in the limit \({\epsilon \searrow 0}\), where \({\alpha \in (0,1)}\) and \({C > 0}\) are determined by \({\mu}\). Derrida and Hilhorst performed a two-scale analysis of the integral equation for the invariant distribution of the Markov chain associated to the matrix product and obtained a probability measure that is expected to be close to the invariant one for small \({\epsilon}\). We introduce suitable norms and exploit contractivity properties to show that such a probability measure is indeed close to the invariant one in a sense that implies a suitable control of the Lyapunov exponent.
Usseglio-carleve Antoine - One of the best experts on this subject based on the ideXlab platform.
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Estimation of risk measures for conditioned elliptical distributions
2018Co-Authors: Usseglio-carleve AntoineAbstract:Cette thèse s'intéresse à l'estimation de certaines mesures de risque d'une Variable aléatoire réelle Y en présence d'une coVariable X. Pour cela, on va considérer que le vecteur (X,Y) suit une loi elliptique. Dans un premier temps, on va s'intéresser aux quantiles de Y sachant X=x. On va alors tester d'abord un modèle de régression quantile assez répandu dans la littérature, pour lequel on obtient des résultats théoriques que l'on discutera. Face aux limites d'un tel modèle, en particulier pour des niveaux de quantile dits extrêmes, on proposera une nouvelle approche plus adaptée. Des résultats asymptotiques sont donnés, appuyés par une étude numérique puis par un exemple sur des données réelles. Dans un second chapitre, on s'intéressera à une autre mesure de risque appelée expectile. La structure du chapitre est sensiblement la même que celle du précédent, à savoir le test d'un modèle de régression inadapté aux expectiles extrêmes, pour lesquels on propose une approche méthodologique puis statistique. De plus, en mettant en évidence le lien entre les quantiles et expectiles extrêmes, on s'aperçoit que d'autres mesures de risque extrêmes sont étroitement liées aux quantiles extrêmes. On se concentrera sur deux familles appelées Lp-quantiles et mesures d'Haezendonck-Goovaerts, pour lesquelles on propose des estimateurs extrêmes. Une étude numérique est également fournie. Enfin, le dernier chapitre propose quelques pistes pour traiter le cas où la taille de la coVariable X est grande. En constatant que nos estimateurs définis précédemment étaient moins performants dans ce cas, on s'inspire alors de quelques méthodes d'estimation en grande dimension pour proposer d'autres estimateurs. Une étude numérique permet d'avoir un aperçu de leurs performancesThis PhD thesis focuses on the estimation of some risk measures for a Real Random Variable Y with a covariate vector X. For that purpose, we will consider that the Random vector (X,Y) is elliptically distributed. In a first time, we will deal with the quantiles of Y given X=x. We thus firstly investigate a quantile regression model, widespread in the litterature, for which we get theoretical results that we discuss. Indeed, such a model has some limitations, especially when the quantile level is said extreme. Therefore, we propose another more adapted approach. Asymptotic results are given, illustrated by a simulation study and a Real data example.In a second chapter, we focus on another risk measure called expectile. The structure of the chapter is essentially the same as that of the previous one. Indeed, we first use a regression model that is not adapted to extreme expectiles, for which a methodological and statistical approach is proposed. Furthermore, highlighting the link between extreme quantiles and expectiles, we Realize that other extreme risk measures are closely related to extreme quantiles. We will focus on two families called Lp-quantiles and Haezendonck-Goovaerts risk measures, for which we propose extreme estimators. A simulation study is also provided. Finally, the last chapter is devoted to the case where the size of the covariate vector X is tall. By noticing that our previous estimators perform poorly in this case, we rely on some high dimensional estimation methods to propose other estimators. A simulation study gives a visual overview of their performance
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Estimation de mesures de risque pour des distributions elliptiques conditionnées
HAL CCSD, 2018Co-Authors: Usseglio-carleve AntoineAbstract:This PhD thesis focuses on the estimation of some risk measures for a Real Random Variable Y with a covariate vector X. For that purpose, we will consider that the Random vector (X,Y) is elliptically distributed. In a first time, we will deal with the quantiles of Y given X=x. We thus firstly investigate a quantile regression model, widespread in the litterature, for which we get theoretical results that we discuss. Indeed, such a model has some limitations, especially when the quantile level is said extreme. Therefore, we propose another more adapted approach. Asymptotic results are given, illustrated by a simulation study and a Real data example.In a second chapter, we focus on another risk measure called expectile. The structure of the chapter is essentially the same as that of the previous one. Indeed, we first use a regression model that is not adapted to extreme expectiles, for which a methodological and statistical approach is proposed. Furthermore, highlighting the link between extreme quantiles and expectiles, we Realize that other extreme risk measures are closely related to extreme quantiles. We will focus on two families called Lp-quantiles and Haezendonck-Goovaerts risk measures, for which we propose extreme estimators. A simulation study is also provided. Finally, the last chapter is devoted to the case where the size of the covariate vector X is tall. By noticing that our previous estimators perform poorly in this case, we rely on some high dimensional estimation methods to propose other estimators. A simulation study gives a visual overview of their performancesCette thèse s'intéresse à l'estimation de certaines mesures de risque d'une Variable aléatoire réelle Y en présence d'une coVariable X. Pour cela, on va considérer que le vecteur (X,Y) suit une loi elliptique. Dans un premier temps, on va s'intéresser aux quantiles de Y sachant X=x. On va alors tester d'abord un modèle de régression quantile assez répandu dans la littérature, pour lequel on obtient des résultats théoriques que l'on discutera. Face aux limites d'un tel modèle, en particulier pour des niveaux de quantile dits extrêmes, on proposera une nouvelle approche plus adaptée. Des résultats asymptotiques sont donnés, appuyés par une étude numérique puis par un exemple sur des données réelles. Dans un second chapitre, on s'intéressera à une autre mesure de risque appelée expectile. La structure du chapitre est sensiblement la même que celle du précédent, à savoir le test d'un modèle de régression inadapté aux expectiles extrêmes, pour lesquels on propose une approche méthodologique puis statistique. De plus, en mettant en évidence le lien entre les quantiles et expectiles extrêmes, on s'aperçoit que d'autres mesures de risque extrêmes sont étroitement liées aux quantiles extrêmes. On se concentrera sur deux familles appelées Lp-quantiles et mesures d'Haezendonck-Goovaerts, pour lesquelles on propose des estimateurs extrêmes. Une étude numérique est également fournie. Enfin, le dernier chapitre propose quelques pistes pour traiter le cas où la taille de la coVariable X est grande. En constatant que nos estimateurs définis précédemment étaient moins performants dans ce cas, on s'inspire alors de quelques méthodes d'estimation en grande dimension pour proposer d'autres estimateurs. Une étude numérique permet d'avoir un aperçu de leurs performance
Yao Jinlan - One of the best experts on this subject based on the ideXlab platform.
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the stability of expectation programming on Real Random Variable
Journal of Guizhou University of Technology, 2006Co-Authors: Yao JinlanAbstract:The stability of expectation programmings with respect to Real Random Variables was generally explored.A complete metric space about the distribution functions was firstly made.Then some properties about expectation programmings were obtained.Based on these results,the stability of expectation programmings on Real Random Variables with the tool of set-valued mappings was explored,and some new results of stability were achieved.
