{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T22:56:47Z","timestamp":1775084207203,"version":"3.50.1"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100014364","name":"Samsung Science and Technology Foundation","doi-asserted-by":"publisher","award":["SSTF-BA2002-03"],"award-info":[{"award-number":["SSTF-BA2002-03"]}],"id":[{"id":"10.13039\/501100014364","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["RS-2023-00301976"],"award-info":[{"award-number":["RS-2023-00301976"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["RS-2024-00333399"],"award-info":[{"award-number":["RS-2024-00333399"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>This paper introduces a novel extension of Fr\u00e9chet means, referred to as generalized Fr\u00e9chet means, as a comprehensive framework for describing the characteristics of random elements. The generalized Fr\u00e9chet mean is defined as the minimizer of a cost function, and the framework encompasses various extensions of Fr\u00e9chet means that have appeared in the literature. The most distinctive feature of the proposed framework is that it allows the domain of minimization for the empirical generalized Fr\u00e9chet means to be random and different from that of its population counterpart. This flexibility broadens the applicability of the Fr\u00e9chet mean framework to various statistical scenarios, including sequential dimension reduction for non-Euclidean data. We establish a strong consistency theorem for generalized Fr\u00e9chet means and demonstrate the utility of the proposed framework by verifying the consistency of principal geodesic analysis on the hypersphere.<\/jats:p>","DOI":"10.1093\/biomet\/asag002","type":"journal-article","created":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T12:28:33Z","timestamp":1768652913000},"source":"Crossref","is-referenced-by-count":1,"title":["Generalized Fr\u00e9chet means with random minimizing domains and its strong consistency"],"prefix":"10.1093","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7710-8537","authenticated-orcid":false,"given":"Jaesung","family":"Park","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6023-8956","authenticated-orcid":false,"given":"Sungkyu","family":"Jung","sequence":"additional","affiliation":[{"name":"Department of Statistics and Institute for Data Innovation in Science, Seoul National University , 1 Gwanak-ro, Gwanak-gu , Seoul 08826,","place":["Republic of Korea"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2026,1,27]]},"reference":[{"key":"2026040117585730400_asag002-B1","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1090\/S0002-9939-2010-10541-5","article-title":"Riemannian $ l^{p} $ center of mass: Existence, uniqueness, and convexity","volume":"139","author":"Afsari","year":"2011","journal-title":"Proc. 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