Papers โบ Estimating Max-Stable Random Vectors with Discrete Spectral Measure using Model-Based...
Estimating Max-Stable Random Vectors with Discrete Spectral Measure using Model-Based Clustering
Alexis Boulin
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This study introduces a novel estimation method for the entries and structure of a matrix A in the linear factor model ๐ = AZ + E. This is applied to an observable vector ๐ โโแต with Z โโแดท, a vector composed of independently regularly varying random variables, and lighter tail noise E โโแต. The spectral measure of the regularly varying random vector ๐ is subsequently discrete and completely characterised by the matrix A. It follows that the behaviour of its maxima can be modelled by a max-stable random vector with discrete spectral measure. Every max-stable random vector with discrete spectral measure can be written as a linear factor model. Each row of the matrix A is supposed to be 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 ๐ 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 ๐. We apply the suggested method to weekly maxima rainfall and wildfires to illustrate its applicability.
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