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Tails of copulas, une lecture graphique
Suite à une formation que je faisais en fin de semaine à Brest (les slides sont ici et là), je voulais revenir sur les histoires de tails of copulas, pour reprendre le titre de l’article (ici) de Gary...
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Lecture notes on risk and insurance
I just finished some lectures notes onrisk and insurance The notes, that can be downloaded here, are in French, and will be used at the JES (Journées d’Etudes Statistiques), organised at the CIRM...
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the Dirichlet distribution
In the course, since we are still introducing some concepts of dependent distributions, we will talk about the Dirichlet distribution, which is a distribution over the simplex of . Let denote the...
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(nonparametric) copula density estimation
Today, we will go further on the inference of copula functions. Some codes (and references) can be found on a previous post, on nonparametric estimators of copula densities (among other related...
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Bounding sums of random variables, part 1
For the last course MAT8886 of this (long) winter session, on copulas (and extremes), we will discuss risk aggregation. The course will be mainly on the problem of bounding the distribution (or some...
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Bounding sums of random variables, part 2
It is possible to go further, much more actually, on bounding sums of random variables (mentioned in the previous post). For instance, if everything has been defined, in that previous post, on...
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Lausanne
I will be back in Lausanne (I was already there last summer) to spend a few days, visiting Florian, at HEC Lausanne. I will also give a talk on old and new results on (standard) families of copulas....
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Copules et processus empiriques
Tarek Zari a soutenu sa thèse au début du mois, présentant une “contribution à l’étude du processus empirique de copule“, et sa thèse est en ligne ici. Je mets aussi une copie des slides de la...
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Fractals and Kronecker product
A few years ago, I went to listen to Roger Nelsen who was giving a talk about copulas with fractal support. Roger is amazing when he gives a talk (I am also a huge fan of his books, and articles), and...
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Course on copulas and correlated risks (in French, still)
The course on copulas, in Luminy, starts at 8.30 on Wednesday (here). The slides can be found here. Arthur CharpentierArthur Charpentier, professor in Montréal, in Actuarial Science. Former...
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Kendall’s function for copulas
As mentioned in the course on copulas, a nice tool to describe dependence it Kendall’s cumulative function. Given a random pair with distribution , define random variable . Then Kendall’s cumulative...
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Copulas estimation and influence of margins
Just a short post to get back on results mentioned at the end of the course. Since copulas are obtained using (univariate) quantile functions in the joint cumulative distribution function, they are –...
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Copulas and tail dependence, part 1
As mentioned in the course last week Venter (2003) suggested nice functions to illustrate tail dependence (see also some slides used in Berlin a few years ago). Slides astin from Arthur Charpentier Joe...
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Copulas and tail dependence, part 2
An alternative to describe tail dependence can be found in the Ledford & Tawn (1996) for instance. The intuition behind can be found in Fischer & Klein (2007)). Assume that and have the same...
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Copulas and tail dependence, part 3
We have seen extreme value copulas in the section where we did consider general families of copulas. In the bivariate case, an extreme value can be written where is Pickands dependence function, which...
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Copules et processus empiriques
Tarek Zari a soutenu sa thèse au début du mois, présentant une “contribution à l’étude du processus empirique de copule“, et sa thèse est en ligne ici. Je mets aussi une copie de ses slides là....
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Exchangeability, credit risk and risk measures
Exchangeability is an extremely concept, since (most of the time) analytical expressions can be derived. But it can also be used to observe some unexpected behaviors, that we will discuss later on with...
View ArticleGraduate Course on Copulas and Extreme Values
This Winter, I will be giving a (graduate) course on extreme values, and copulas (more generally multivariate models and dependence), MAT8595. It is an ISM course, and even if it will probably be given...
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Conditional dependence measures
This week, I spend some time at the Workshop on Nonparametric Curve Smoothing conference at Concordia. Yesterday afternoon, Noël Veraverbeke show an interesting graph, to illustrate conditional copulas...
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In statistics, having too much information might not be a good thing
A common idea in statistics is that if we don’t know something, and we use anestimator of that something (instead of the true value) then there will be some additional uncertainty. For instance,...
View ArticleMultivariate Archimax copulas
Our paper, written jointly also with Anne-Laure Fougères, Christian Genest and Johanna Nešlehová, entitled Multivariate Archimax Copulas, should appear some day in the Journal of Multivariate Analysis....
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Bivariate Densities with N(0,1) Margins
This Monday, in the ACT8595 course, we came back on elliptical distributions and conditional independence (here is an old post on de Finetti’s theorem, and the extension to Hewitt-Savage’s). I have...
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Talk at CIMAT, Guanajuato, Mexico
I will be back in Guanajuato, Mexico, this week, to visit Victor Rivero. And I will give a talk at the Centro de Investigacion en Matematicas (CIMAT) this Wednesday on “Multivariate Archimax Copulas“....
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Correlation with constraints on pairs
An interesting question was posted on http://math.stackexchange.com/726205/…: if one knows the covariances and , is it possible to infer ? I asked myself a question close to this one a few weeks ago...
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Modeling the Marginals and the Dependence separately
When introducing copulas, it is commonly admitted that copulas are interesting because they allow to model the marginals and the dependence structure separately. The motivation is probably Sklar’s...
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Copula Density Estimation
The joint paper, written with Gery Geenens and Davy Paindaveine, entitled “Probit transformation for nonparametric kernel estimation of the copula density” is now online on...
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Examen, Copules et Valeurs Extrêmes
Après les exposés des dernières séances, l’examen du cours MAT8595, Copules et Valeurs Extrêmes avait lieu hier matin. L’énoncé est en ligne, et j’ai aussi écrit quelques éléments de correction, là. En...
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On Hoeffding’s identity
In 1940, Wassily Hoeffding published Masstabinvariante Korrelationstheorie, which was an impressive paper. For those (like me) who unfortunately barely speak German, an English translation could be...
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Conditional Distributions from some Elliptical Vectors
This winter, in my ACT8595 course, I asked my students (that was some homework) to prove that it was possible to derive the conditional distribution when we have a Student-t random vector (and to get...
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The Pay-for-Performance Myth
Last week, Eric Chemi and Ariana Giorgi published an interesting article on “The Pay-for-Performance Myth” With all the public chatter about exorbitant executive compensation and income inequality,...
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