Hier, Dafnis Krasniqi défendait sa thèse de doctorat à l’université Paris Sorbonne. Félicitations Dafnis !
Tag Archives: PhD
MSc and PhD scolarships
Defense de doctorat d’Amadou Diogo Barry
Ce jeudi matin, Amadou Diogo Barry défendra sa thèse de doctorat sur la régression expectile pour l’analyse de données longitudinales.
Advanced Econometrics: Quantiles and Expectiles
Next Thursday, I will give the fourth lecture of the PhD course on advanced tools for econometrics, on quantile and expectile regressions. Slides are available online.
Advanced Econometrics: Model Selection
On Thursday, March 23rd, I will give the third lecture of the PhD course on advanced tools for econometrics, on model selection and variable selection, where we will focus on ridge and lasso regressions . Slides are available online.
The first part was on on Nonlinearities in Econometric models, and the second one on Simulations.
Advanced Econometrics: Nonlinearities
On Thursday, March 2nd, I will give the first lecture of the PhD course on advanced tools for econometrics, on nonlinearities. Slides are available online.
Soutenance de thèse sur les inégalités
Ce jeudi, je participais au jury de thèse de Fattouma Souissi en tant que rapporteur, à l’université de Montpellier, sur les régressions PLS-Gini. Le manuscript de la thèse est désormais en ligne.
PhD defense, in Louvain
I was, this morning, at the (private) PhD defense of Mathieu Pigeon, at UCL, Université Cathololique de Louvain. Mathieu obtained some very interesting results on claims reserving based on individual observations. I will try to upload the slides of his defense, someday.
Amsterdam, PhD defense
Last week, I was involved in the PhD defense of Julien Tomas, with Rob Kaas (promotor), Frédéric Planchet (co-promotor), Katrien Antonio, Marc Goovaerts, Ann De Schepper and Michel Vellekoop. The PhD thesis – untitled quantifying biometric life insurance risks with non-parametric smoothing methods – can be dowloaded on http://dare.uva.nl/… and on http://tel.archives-ouvertes.fr/.
The R codes will be available soon on my blog (and on Julien’s new website http://www.likelihood.me/).
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PhD defense on copulas
This Wednesday I will be at Université Paris 1 Sorbonne as a member of the jury of the PhD thesis of Pierre-André Maugis, on conditional correlation and vine copula.
Vine copulas were born in 2002 with thepaper of Tim Bedford and Roger M. CookeVines–a new graphical model for dependent random variables. The idea is to use the following decomposition for a multivariate density
(from Bayes formula, with synthetic notations). Then using the relationship between a bivariate density and its copula (density)
thus
Using again Bayes formula,
and we can write
Since and
, the previous expression becomes
or to stress on the most important part (as I see it)
It is common then to assume that this conditional copula does not depend on the conditioning parameter. The more detailed expression of that joint trivariate density is
The (parametric) inference algorithm is defined in Cooke, Joe and Aas (2010) as follows
The important assumption in vine copula models is that conditional copulas are constant. And this assumption might be relevant in some cases. For instance, in the Gaussian case (the observations have a Gaussian joint distribution – or at least copula – and we fit a vine model with Gaussian bivariate copulas).
The code to fit a vine copula is the following,
> library(CDVine) > library(mnormt) > SIGMA=matrix(c(1,.6,.7,.6,1,.8,.7,.8,1),3,3) > X=rmnorm(n=100000,varcov=SIGMA) > CDVineSeqEst(dat=X, family = c(1,1,1), + type = 1, method = "mle") $par [1] 0.6001505 0.7023699 0.6698215 $par2 [1] 0 0 0
Note that it is consistent with the following algorithm where conditional copulas are fitted. In the following, for all values of the given component, we wit a Gaussian copula for the conditional remaining pair,
> U=pnorm(X) > U1U2=U[,1:2] > U1U3=U[,c(1,3)] > GaussCop = normalCopula(param=.5, dim = 2) > U1U2=U[,1:2] > U1U3=U[,c(1,3)] > fit12.mpl = fitCopula(GaussCop, U1U2, method="mpl")@estimate > fit13.mpl = fitCopula(GaussCop, U1U3, method="mpl")@estimate > fit12.mpl [1] 0.5984932 > fit13.mpl [1] 0.7005185 > fit23a=fit23b=rep(NA,99) > for(i in 4:96){ + x=i/100 + C12=pcopula(normalCopula(param=fit12.mpl, dim = 2),U1U2) + C13=pcopula(normalCopula(param=fit13.mpl, dim = 2),U1U3) + U12=rank(C12)/(nrow(U)+1) + U13=rank(C13)/(nrow(U)+1) + U23=cbind(U12[abs(U[,1]-x)<.02],U13[abs(U[,1]-x)<.02]) + V23=cbind(rank(U23[,1])/(nrow(U23)+1), + rank(U23[,2])/(nrow(U23)+1)) + fit23.mpl = fitCopula(GaussCop, V23, method="mpl")@estimate + fit23a[i]=fit23.mpl + } > plot(X,fit23a,col="red")
It looks like assuming the conditional copula as constant was a valid assumption here
But note that if the true distribution is not Gaussian, then assuming the conditional copula as constant is not valid anymore (here a trivariate Clayton copula was generated)
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 soutenance là. Historiquement, il semble que Frits Ruymgaart a été le premier a parler de processus empirique de copules, en 1973 (sa thèse est en ligne ici).
Paul Deheuvels avait également introduit la notion en copule empirique dès 1979 sous le nom de “fonction de dépendance empirique“. A la même époque, Ludger Rüschendorf proposait également une étude asymptotique des processus empiriques de copules (ici en 1976), ou encore Gäenssler et Stute dans leur seminar on empirical processes et Winfried Stute dans les années 80 (là). Une revue de la littérature sur les processus empiriques multivariés a été publié à cette époque, en ligne là. Depuis Jean-David Fermanian a publié un papier ici sur la convergence faible, et Paul Deheuvels ou Ludger Rüschendorf ont publié énormément de choses, en particulier sur la vitesse de convergence…
Soutenance de thèse, Paris II
Soutenance de thèse de Noureddine Ben Lagha, à Paris II Assas, sur l’assurance automobile,
Son directeur de thèse était Michel Grun-Rehomme, avec dans le jury, Georges Bresson, Alain Trognon, Michel, Marc Fleurbaey et Denis Fougère.