{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T07:36:12Z","timestamp":1784273772583,"version":"3.55.0"},"reference-count":11,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T00:00:00Z","timestamp":1772582400000},"content-version":"vor","delay-in-days":62,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In this paper, we characterize the extremal dependence of $ d $ asymptotically dependent variables using a class of random vectors on the $ (d-1) $-dimensional hyperplane perpendicular to the diagonal vector $ \\mathbf{1}=(1,\\ldots,1) $. This translates analyses of multivariate extremes to analyses on a linear vector space, opening up possibilities for applying existing statistical techniques based on linear operations. As an example, we demonstrate how to obtain lower-dimensional approximations of tail dependence through principal component analysis. Additionally, we show that the widely used H\u00fcsler\u2013Reiss family is characterized by a Gaussian family residing on the hyperplane.<\/jats:p>","DOI":"10.1093\/biomet\/asag015","type":"journal-article","created":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T12:53:13Z","timestamp":1771505593000},"source":"Crossref","is-referenced-by-count":2,"title":["Characterizing extremal dependence on a hyperplane"],"prefix":"10.1093","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9825-3422","authenticated-orcid":false,"given":"P","family":"Wan","sequence":"first","affiliation":[{"name":"Department of Econometrics, Erasmus School of Economics, Erasmus University Rotterdam , Burg. 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