Séance Séminaire

Séminaire des Doctorant·e·s

Estimating Max-Stable Random Vectors with Discrete Spectral Measure using Model-Based Clustering

This study introduces a novel estimation method for the entries and structure of a matrix A in the linear factor model X = A*Z + E. This is applied to an observable vector X in R^d with Z in R^K, a vector composed of independently regularly varying random variables, and light-tailed independent noise E in R^d. This leads to max-linear models treated in classical multivariate extreme value theory. The spectral measure of the limit distribution is subsequently discrete and completely characterized by the matrix A. Every max-stable random vector with discrete spectral measure can be written as a max-linear model. Each row of the matrix A is both scaled and sparse. Additionally, the value of K is not known a priori. The problem of identifying the matrix A from its matrix of pairwise extremal correlation is addressed. In the presence of pure variables, which are elements of X linked, through A, to a single latent factor, the matrix A can be reconstructed from the extremal correlation matrix. Our proofs of identifiability are constructive and pave the way for our innovative estimation for determining the number of factors K and the matrix A from n weakly dependent observations on X.