{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/estimating-max-stable-random-vectors-with","title":"Estimating Max-Stable Random Vectors with Discrete Spectral Measure using Model-Based Clustering","arxiv_id":"2402.01609","date":"2024-02-02","proceeding":null,"authors":["Alexis Boulin"],"abstract":"This study introduces a novel estimation method for the entries and structure of a matrix $A$ in the linear factor model $\\mathbf{X} = A\\textbf{Z} + \\textbf{E}$. This is applied to an observable vector $\\mathbf{X} \\in \\mathbb{R}^d$ with $\\textbf{Z} \\in \\mathbb{R}^K$, a vector composed of independently regularly varying random variables, and lighter tail noise $\\textbf{E} \\in \\mathbb{R}^d$. The spectral measure of the regularly varying random vector $\\mathbf{X}$ 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 $\\mathbf{X}$ 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 $\\mathbf{X}$. We apply the suggested method to weekly maxima rainfall and wildfires to illustrate its applicability.","url_abs":"https://arxiv.org/abs/2402.01609v4","url_pdf":"https://arxiv.org/pdf/2402.01609v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"estimating-max-stable-random-vectors-with","repo_url":"https://github.com/aleboul/linear_factor_models","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}