{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,28]],"date-time":"2026-10-28T15:18:21Z","timestamp":1793200701205,"version":"4.5.0"},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,7,18]],"date-time":"2025-07-18T00:00:00Z","timestamp":1752796800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001691","name":"JSPS KAKENHI","doi-asserted-by":"publisher","award":["JP23K12456"],"award-info":[{"award-number":["JP23K12456"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>There has been growing interest in statistical analysis of random objects taking values in a non-Euclidean metric space. One important class of such objects consists of data on manifolds. This article is concerned with inference on the Fr\u00e9chet mean and related population objects on manifolds. We develop the concept of nonparametric likelihood for data on manifolds and propose general inference methods by adapting the theory of empirical likelihood. In addition to the basic asymptotic properties, such as Wilks\u2019 theorem of the empirical likelihood statistic, we present several generalizations of the proposed methodology: two-sample testing, inference on the Fr\u00e9chet variance, quasi-Bayesian inference, local Fr\u00e9chet regression, and estimation of the Fr\u00e9chet mean set. Simulation and real data examples illustrate the usefulness of the proposed methodology and its advantage against the conventional Wald test.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkaf043","type":"journal-article","created":{"date-parts":[[2025,7,18]],"date-time":"2025-07-18T17:16:01Z","timestamp":1752858961000},"page":"91-119","source":"Crossref","is-referenced-by-count":1,"title":["Empirical likelihood for manifolds"],"prefix":"10.1093","volume":"88","author":[{"given":"Daisuke","family":"Kurisu","sequence":"first","affiliation":[{"name":"Center for Spatial Information Science, The University of Tokyo , 5-1-5, Kashiwanoha, Kashiwa-shi, Chiba 277-8568 ,","place":["Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Taisuke","family":"Otsu","sequence":"additional","affiliation":[{"name":"Department of Economics, London School of Economics , Houghton Street, London WC2A 2AE 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