{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T11:09:55Z","timestamp":1782126595237,"version":"3.54.5"},"reference-count":41,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T00:00:00Z","timestamp":1678320000000},"content-version":"vor","delay-in-days":129,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address this problem, we introduce Covariance Networks (CovNet) as a modelling and estimation tool. The CovNet model is universal\u2014it can be used to approximate any covariance up to desired precision. Moreover, the model can be fitted efficiently to the data and its neural network architecture allows us to employ modern computational tools in the implementation. The CovNet model also admits a closed-form eigendecomposition, which can be computed efficiently, without constructing the covariance itself. This facilitates easy storage and subsequent manipulation of a covariance in the context of the CovNet. We establish consistency of the proposed estimator and derive its rate of convergence. The usefulness of the proposed method is demonstrated via an extensive simulation study and an application to resting state functional magnetic resonance imaging data.<\/jats:p>","DOI":"10.1111\/rssb.12551","type":"journal-article","created":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T23:46:45Z","timestamp":1667260005000},"page":"1785-1820","source":"Crossref","is-referenced-by-count":7,"title":["CovNet: Covariance Networks for Functional Data on Multidimensional Domains"],"prefix":"10.1093","volume":"84","author":[{"given":"Soham","family":"Sarkar","sequence":"first","affiliation":[{"name":"Theoretical Statistics and Mathematics Unit , , New Delhi , India"},{"name":"Indian Statistical Institute, Delhi Centre , , New Delhi , India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Victor M.","family":"Panaretos","sequence":"additional","affiliation":[{"name":"Institut de Math\u00e9matiques , , Lausanne , Switzerland"},{"name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , , Lausanne , Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,10,31]]},"reference":[{"key":"2023030906300487500_","volume-title":"Random fields and geometry","author":"Adler","year":"2007"},{"key":"2023030906300487500_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511624216","volume-title":"Neural network learning: theoretical foundations","author":"Anthony","year":"1999"},{"key":"2023030906300487500_","first-page":"1906","article-title":"Evaluating stationarity via change-point alternatives with applications to fMRI data","author":"Aston","year":"2012","journal-title":"The Annals of Applied Statistics"},{"key":"2023030906300487500_","doi-asserted-by":"crossref","first-page":"1431","DOI":"10.1214\/16-AOS1495","article-title":"Tests for separability in nonparametric covariance operators of random surfaces","volume":"45","author":"Aston","year":"2017","journal-title":"The 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