{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:21:34Z","timestamp":1760242894933,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2016,10,20]],"date-time":"2016-10-20T00:00:00Z","timestamp":1476921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"German Research Foundation","award":["Open Access Publication Fund TU Ilmenau"],"award-info":[{"award-number":["Open Access Publication Fund TU Ilmenau"]}]},{"name":"Klaus Tschira Stiftung, gemeinn\u00fctzige Gesellschaft","award":["03.126.2016"],"award-info":[{"award-number":["03.126.2016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding\u2019s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that they require no distributional assumptions. These are then compared with asymptotic confidence sets in simulations and for a real data set.<\/jats:p>","DOI":"10.3390\/e18100375","type":"journal-article","created":{"date-parts":[[2016,10,20]],"date-time":"2016-10-20T10:15:49Z","timestamp":1476958549000},"page":"375","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Non-Asymptotic Confidence Sets for Circular Means"],"prefix":"10.3390","volume":"18","author":[{"given":"Thomas","family":"Hotz","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Ilmenau, 98684 Ilmenau, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florian","family":"Kelma","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Ilmenau, 98684 Ilmenau, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Johannes","family":"Wieditz","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Ilmenau, 98684 Ilmenau, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,20]]},"reference":[{"key":"ref_1","unstructured":"Mardia, K.V. (1972). Directional Statistics, Academic Press."},{"key":"ref_2","unstructured":"Watson, G.S. (1983). Statistics on Spheres, Wiley."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Fisher, N.I. (1993). Statistical Analysis of Circular Data, Cambridge University Press.","DOI":"10.1017\/CBO9780511564345"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Jammalamadaka, S.R., and SenGupta, A. (2001). Topics in Circular Statistics, World Scientific.","DOI":"10.1142\/9789812779267"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mardia, K.V., and Jupp, P.E. (2000). Directional Statistics, Wiley.","DOI":"10.1002\/9780470316979"},{"key":"ref_6","first-page":"215","article-title":"Les \u00e9l\u00e9ments al\u00e9atoires de nature quelconque dans un espace distanci\u00e9","volume":"10","year":"1948","journal-title":"Annales de l\u2019Institut Henri Poincar\u00e9"},{"key":"ref_7","unstructured":"Hotz, T. (2013, January 28\u201330). Extrinsic vs. Intrinsic Means on the Circle. Proceedings of the 1st Conference on Geometric Science of Information, Paris, France. Lecture Notes in Computer Science, Volume 8085."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1090\/S0002-9939-2010-10541-5","article-title":"Riemannian Lp center of mass: Existence, uniqueness, and convexity","volume":"139","author":"Afsari","year":"2011","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.3150\/15-BEJ728","article-title":"A stochastic algorithm finding p-means on the circle","volume":"22","author":"Arnaudon","year":"2016","journal-title":"Bernoulli"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1017\/S0266466605050036","article-title":"Model selection and inference: Facts and fiction","volume":"21","author":"Leeb","year":"2005","journal-title":"Econ. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/01621459.1963.10500830","article-title":"Probability Inequalities for Sums of Bounded Random Variables","volume":"58","author":"Hoeffding","year":"1963","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Boucheron, S., Lugosi, G., and Massart, P. (2013). Concentration Inequalities : A Nonasymptotic Theory of Independence, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199535255.001.0001"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Nielsen, F., and Barbaresco, F. (2015, January 28\u201330). Universal, Non-asymptotic Confidence Sets for Circular Means. Proceedings of the 2nd International Conference on Geometric Science of Information, Palaiseau, France. Lecture Notes in Computer Science, Volume 9389.","DOI":"10.1007\/978-3-319-25040-3"},{"key":"ref_14","unstructured":"R Core Team (2013). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing. version 2.15.3."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1007\/BF00297947","article-title":"Die optische Richtungsorientierung der Roten Waldameise (Formica Rufa L.)","volume":"40","author":"Jander","year":"1957","journal-title":"Zeitschrift f\u00fcr Vergleichende Physiologie"},{"key":"ref_16","unstructured":"Fernandez-Duran, J.J., and Gregorio-Dominguez, M.M. (CircNNTSR: An R Package for the Statistical Analysis of Circular Data Using Nonnegative Trigonometric Sums (NNTS) Models, 2013). CircNNTSR: An R Package for the Statistical Analysis of Circular Data Using Nonnegative Trigonometric Sums (NNTS) Models, version 2.1."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/10\/375\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:33:35Z","timestamp":1760211215000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/10\/375"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,20]]},"references-count":16,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2016,10]]}},"alternative-id":["e18100375"],"URL":"https:\/\/doi.org\/10.3390\/e18100375","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2016,10,20]]}}}