{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T18:31:43Z","timestamp":1791052303431,"version":"4.1.0"},"reference-count":36,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2009,6,1]],"date-time":"2009-06-01T00:00:00Z","timestamp":1243814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,6,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulas a correlation-like structure remains, but different margins and non-existence of moments are possible. After introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behaviour of the statistics can be observed even for small sample sizes. Finally, we show our method at work for a financial data set and explain differences between our copula-based approach and the classical approach. Our new method yielear models also.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2009.00707.x","type":"journal-article","created":{"date-parts":[[2009,6,1]],"date-time":"2009-06-01T10:13:21Z","timestamp":1243851201000},"page":"737-753","source":"Crossref","is-referenced-by-count":27,"title":["Copula Structure Analysis"],"prefix":"10.1093","volume":"71","author":[{"given":"Claudia","family":"Kl\u00fcppelberg","sequence":"first","affiliation":[{"name":"Technische Universit\u00e4t M\u00fcnchen , Garching , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gabriel","family":"Kuhn","sequence":"additional","affiliation":[{"name":"Technische Universit\u00e4t M\u00fcnchen , Garching , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2009,6,1]]},"reference":[{"key":"2023032921205175900_","volume-title":"An Introduction to Multivariate Statistical Analysis","author":"Anderson","year":"2003"},{"key":"2023032921205175900_","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1146\/annurev.psych.47.1.563","article-title":"Covariance structure analysis: statistical practice, theory and directions","volume":"47","author":"Bentler","year":"1996","journal-title":"A. 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