En salle de séminaire du LPMA, à Jussieu (salle Paul Lévy, 16-26-113)
Jeudi 10 mars (14h) : Bojan BASRAK (Université de Zagreb), On tail process and its role in limit theorems
We discuss how tail process captures dependence structure ina stationary regularly varying sequence. This theory is applied to extend limiting results for corresponding point processes from iid to dependent sequences, as long as their dependence declines in time. We will also discuss the convergence of partial sums and other functionals of regularly varying sequences, covering some recent results in the literature.
Jeudi 7 avril (14h) : Enkelejd HASHORVA (HEC, Lausanne), Parisian Ruin and Parisian Ruin Time -- Approximations for Gaussian Risk Models (joint work with K. Debicki and L. Ji)
The concept of Parisian ruin is relatively new in risk theory. In the literature few results are known for the probability of Parisian ruin on infinite time-horizon Lévy risk processes. In this talk we are primarily concerned with the approximation of Parisian ruin probability and Parisian ruin time in the framework of Gaussian risk models. Our results cover the infinite-time horizon when the underlying Gaussian process is self-similar, whereas for the finite time-horizon our Gaussian risk model is quite general.
Jeudi 14 avril (14h) : Christian Yann ROBERT (ISFA, Université Lyon 1), Cluster size distributions of extreme values for the Poisson-Voronoi tessellation (joint work with Nicolas CHENAVIER)
We consider the Voronoi tessellation based on a stationary Poisson process in Rd. We are interested in extremes of geometric characteristics of the tesselation and focus on the asymptotic distribution of the number of cells with extreme values. We provide a characterization of the asymptotic cluster size distribution which is based on the behavior of neighbouring cells of the typical cell when the geometric characteristic of the typical cell is extreme.
Jeudi 12 mai (14h) : Jan BEIRLANT (KU Leuven and University of the Free State) Fitting tails affected by truncation
Joint work with T. Reynkens (KU Leuven) and I. Fraga Alves (University of Lisbon)
In several applications, ultimately at the largest data, truncation effects can be observed when analyzing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as the Gutenberg-Richter relation in geophysics, while at other instances the nature of the measurement process itself may cause under recovery of large values, for instance due to flooding in river discharge readings. Recently Beirlant, Fraga Alves and Gomes (Extremes, 2016) discussed tail fitting for truncated Pareto-type distributions. Using examples from earthquake analysis, hydrology and diamond valuation we demonstrate the need for a unified treatment of extreme value analysis for truncated heavy and light tails.
Jeudi 2 juin (14h) : Kirstin STROKORB (Université de Mannheim) Some connections between max-stable processes, random sets and risk measures
Joint work with Ilya Molchanov
In the past decade max-stable processes have gained particular interest in connection with the annual maxima method in order to assess spatial extremal scenarios such as heavy rainfall. In this context (bivariate) extremal coefficients are usually considered as an important summary measure. Here, we show how its spatial analogue, the extremal coefficient functional, stands in a one-to-one correspondence with max-stable processes generated from random sets. To this end, it is natural and convenient to work with max-stable processes with upper semi-continuous sample paths, or equivalently, with max-stable random sup-measures. We show how the max-stable random sup-measures generated from random sets can be seen as a benchmark in the space of all such sup-measures and reveal connections to the theory of utility functions (or risk-measures). Finally, we give a shorter proof for some known properties of the argmax-set in continuous choice models.
Jeudi 9 juin (14h-16h) : Anne SABOURIN (Télécom ParisTech) Statistical learning tools for multivariate extremes, applications to dimension reduction and anomaly detection
Joint work with Maël Chiapino, Nicolas Goix, Stephan Clémençon
The dependence structure of multivariate extreme events of multivariate nature is a major concern for risk management. In a high dimensional context (d>50), dimension reduction is a natural first step. Recent works (Goix et al., 2015,2016) have defined sparsity in multivariate extremes as the concentration of the exponent measure (a convenient characterization of extremal dependence) on low dimensional subspaces of R^d, and have proposed an algorithm allowing to recover its support when the latter is sparse.
In this talk, we consider situations where the above mentioned approach breaks down because no clear sparsity pattern emerges from the data. We propose an alternative dependence criterion allowing to gather together different subspaces that are "close" to each other, in the sense that they have many non-zero coordinates in common. The resulting "feature clustering" algorithm aims at recovering the maximal subgroups of features that are "dependent at extreme level", i.e. that are likely to take extreme values simultaneously. To bypass the computational issues that arise when it comes to dealing with possibly O(2^d) groups of features, the graphical structure stemming from the definition of the clusters is exploited, which reduces drastically the number of subgroups on which the estimation procedure has to be performed. Results on simulated and real data show that our method allows to recover a meaningful summary of the dependence structure of extremes in a reasonable amount of computational time.