{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,25]],"date-time":"2026-10-25T15:42:54Z","timestamp":1792942974225,"version":"4.5.0"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2019,6,19]],"date-time":"2019-06-19T00:00:00Z","timestamp":1560902400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Decadal and Regional Climate Prediction Using Earth System Models Program"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,9,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We propose two decompositions that help to summarize and describe high-dimensional tail dependence within the framework of regular variation. We use a transformation to define a vector space on the positive orthant and show that transformed-linear operations applied to regularly-varying random vectors preserve regular variation. We summarize tail dependence via a matrix of pairwise tail dependence metrics that is positive semidefinite; eigendecomposition allows one to interpret tail dependence in terms of the resulting eigenbasis. This matrix is completely positive, and one can easily construct regularly-varying random vectors that share the same pairwise tail dependencies. We illustrate our methods with Swiss rainfall and financial returns data.<\/jats:p>","DOI":"10.1093\/biomet\/asz028","type":"journal-article","created":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T07:09:39Z","timestamp":1557904179000},"page":"587-604","source":"Crossref","is-referenced-by-count":80,"title":["Decompositions of dependence for high-dimensional extremes"],"prefix":"10.1093","volume":"106","author":[{"given":"D","family":"Cooley","sequence":"first","affiliation":[{"name":"Department of Statistics, Colorado State University, Fort Collins, Colorado, U S A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E","family":"Thibaud","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 8, Lausanne, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,6,19]]},"reference":[{"key":"2020061820032940300_B1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/S0024-3795(02)00250-1","article-title":"The maximal cp-rank of rank $k$ completely positive matrices.","volume":"363","author":"Barioli,","year":"2003","journal-title":"Lin. 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