[Statlist] Research Seminar in Statistics *FRIDAY, 30 SEPTEMBER 2022* GSEM, University of Geneva

[gsem-support-instituts]

Dear All,

We are pleased to invite you to our next Research Seminar.

Looking forward to seeing you,


Organized by Professor Sebastian Engelke on behalf of the Research Center for Statistics (https://www.unige.ch/gsem/en/research/institutes/rcs/)


FRIDAY, 30 SEPTEMBER 2022 at 11:15am, Uni-Mail M 5220 & ONLINE
Zoom research webinar: https://unige.zoom.us/j/92924332087?pwd=U1U1NFk4dTFCRHBMeWYrSDBQcXBiQT09
Meeting ID: 929 2433 2087
Passcode: 399192

Total Positivity in Multivariate Extremes
(jointly with Sebastian Engelke and Piotr Zwiernik)
Frank ROETTGER, GSEM
https://www.unige.ch/gsem/en/research/faculty/fellows/frank-roettger/

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.


Visit the website: https://www.unige.ch/gsem/en/research/seminars/rcs/