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We document new conditions that establish identification for several nonindependent component models, for example, common variance models, and propose efficient estimation methods based on the identification results. We show that in situations where independence cannot be assumed the efficiency gains can be significant relative to methods that rely on independence.<\/jats:p>","DOI":"10.1214\/24-aos2373","type":"journal-article","created":{"date-parts":[[2024,12,19]],"date-time":"2024-12-19T01:19:57Z","timestamp":1734571197000},"page":"2506-2528","source":"Crossref","is-referenced-by-count":10,"title":["Non-independent component analysis"],"prefix":"10.1214","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6996-9520","authenticated-orcid":false,"given":"Geert","family":"Mesters","sequence":"first","affiliation":[{"name":"Department of Economics and Business, Universitat Pompeu Fabra"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3431-131X","authenticated-orcid":false,"given":"Piotr","family":"Zwiernik","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences, University or Toronto"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"63","doi-asserted-by":"publisher","unstructured":"Vogel, D.<\/small> and Fried, R.<\/small> (2011). 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