{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T17:46:30Z","timestamp":1786470390740,"version":"build-2736575974"},"reference-count":36,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T00:00:00Z","timestamp":1786406400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007431","name":"NRF","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007431","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Korean government","award":["RS-2026-25468563"],"award-info":[{"award-number":["RS-2026-25468563"]}]},{"name":"Basic Science Research Program"},{"name":"G-LAMP Program"},{"DOI":"10.13039\/100009122","name":"Ministry of Education","doi-asserted-by":"publisher","award":["RS-2021-NR060140"],"award-info":[{"award-number":["RS-2021-NR060140"]}],"id":[{"id":"10.13039\/100009122","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009122","name":"Ministry of Education","doi-asserted-by":"publisher","award":["RS-2025-25441317"],"award-info":[{"award-number":["RS-2025-25441317"]}],"id":[{"id":"10.13039\/100009122","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We propose a notion of geometric quantiles on Hadamard spaces, or global non-positive curvature spaces. After providing some definitions and basic properties, including scaled isometry equivariance and a necessary condition on the gradient of the quantile loss function, we investigate asymptotic properties, such as strong consistency and joint asymptotic normality. We provide a detailed description of how to compute quantiles using a gradient descent algorithm in hyperbolic space. We detail several potential uses for these quantiles\u2014defining measures of distributional characteristics, detecting outliers via a transformation\u2013retransformation procedure, and testing the equality of distributions\u2014and demonstrate their application through simulations and real biological data.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag121","type":"journal-article","created":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:58:40Z","timestamp":1785412720000},"source":"Crossref","is-referenced-by-count":0,"title":["Quantiles on global non-positive curvature spaces"],"prefix":"10.1093","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-4821-2490","authenticated-orcid":false,"given":"Ha-Young","family":"Shin","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial Science, Soongsil University , Seoul 06978 ,","place":["Korea"]},{"name":"Integrative Institute of Basic Sciences, Soongsil University , Seoul 06978 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