{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T20:14:33Z","timestamp":1762460073620,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,7]],"date-time":"2022-01-07T00:00:00Z","timestamp":1641513600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003407","name":"Ministry of Education, Universities and Research","doi-asserted-by":"publisher","award":["HiDiNet"],"award-info":[{"award-number":["HiDiNet"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We use a recently proposed fast test of copula radial symmetry based on multiplier bootstrap and obtain an equivalent randomization test. The literature shows the statistical superiority of the randomization approach in the bivariate case. We extend the comparison of statistical performance focusing on the high-dimensional regime in a simulation study. We document radial asymmetry in the joint distribution of the percentage changes of sectorial industrial production indices of the European Union.<\/jats:p>","DOI":"10.3390\/sym14010097","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T23:35:09Z","timestamp":1641771309000},"page":"97","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["High-Dimensional Radial Symmetry of Copula Functions: Multiplier Bootstrap vs. Randomization"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6690-0832","authenticated-orcid":false,"given":"Monica","family":"Billio","sequence":"first","affiliation":[{"name":"Department of Economics, University Ca\u2019 Foscari of Venice, 30123 Venice, Italy"}]},{"given":"Lorenzo","family":"Frattarolo","sequence":"additional","affiliation":[{"name":"Unit B.1, Joint Research Centre (JRC), European Commission, 21027 Ispra, Italy"}]},{"given":"Dominique","family":"Gu\u00e9gan","sequence":"additional","affiliation":[{"name":"Department of Economics, University Ca\u2019 Foscari of Venice, 30123 Venice, Italy"},{"name":"Centre d\u2019Economie de la Sorbonne, University Paris-1 Panth\u00e9on-Sorbonne, 75647 Paris, France"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1080\/10485259308832574","article-title":"Some concepts of bivariate symmetry","volume":"3","author":"Nelsen","year":"1993","journal-title":"J. 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