Total Positivity in Multivariate Extremes

30.09.2022 11:15 – 12:15

RESEARCH CENTER FOR STATISTICS SEMINAR / ABSTRACT

Engelke and Hitz (2020, JRSSB) recently introduced a general theory for conditional independence and graphical models for extremes. For Hüsler--Reiss distributions, the extremal analogue of Gaussians, it follows that their precision matrices similarly to Gaussians encode the extremal graphical structure.

Multivariate total positivity of order 2 (MTP2) is a strong form of positive dependence that induces many interesting properties in graphical modeling. A multivariate Gaussian is MTP2 when its precision matrix is an M-matrix, i.e. when all the non-diagonal entries in the precision matrix are non-positive. We introduce the notion of extremal MTP2 (EMTP2) and show that many classical models are always EMTP2. A Hüsler--Reiss random vector is EMTP2 if and only if its precision matrix is the Laplacian matrix of a connected graph with positive edge weights. We propose an estimator for the parameters of the Hüsler--Reiss distribution under EMTP2 as the solution of a convex optimization problem with Laplacian constraint. We prove that this estimator is consistent and typically yields a sparse model with possibly non-decomposable extremal graphical structure. We construct a block descent algorithm and demonstrate on real data that our EMTP2 estimator outperforms other available graphical estimators.

Lieu

Bâtiment: Uni Mail

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Boulevard du Pont-d'Arve 40
1205 Geneva

Room M 5220, 5th floor

Organisé par

Faculté d'économie et de management
Research Center for Statistics

Intervenant-e-s

Frank ROETTGER, GSEM

entrée libre

Classement

Catégorie: Séminaire

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