Statistics and Risk Management Seminar - 24/07/2013

Wednesday, 24 July 2013, 2:00 p.m.

Lecturer: Doutor Miguel de Carvalho, Pontificia Universidad Católica de Chile

Title: "Multivariate Extremes: Modeling, Smoothing, and Regression".

Local: Anfiteatro 2 A, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: In this talk I discuss smoothing methods for the spectral measure of an extreme-value distribution. A complex issue in conducting inference over this setting is that the spectral measure needs to obey a certain moment condition. A Euclidean likelihood-based estimator for the spectral measure is discussed, and it is shown to have the same limit distribution as the maximum empirical likelihood estimator of Einmahl and Segers, Ann. Statist. 37, 2953–2989 (2009). For real data applications smooth versions of the empirical estimator may be preferred, but these can be readily constructed by suitably convoluting the weights of our empirical likelihood-based method with a kernel on the simplex. I use this setup for developing a regression model for the spectral measure itself, and illustrate the methods in an extreme temperature data analysis.