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We establish consistency and rates of convergence for various estimators of S and its boundary. This problem has relevant applications in ecology in estimating the home range of an animal on the basis of tracking data. There are a variety of studies on the habitat of animals that employ the notion of home range. The paper offers theoretical foundations for a new methodology that, under fairly unrestrictive shape assumptions, allows us to find flexible regions close to reality. The theoretical findings are illustrated on simulated and real data examples.<\/jats:p>","DOI":"10.1111\/rssb.12149","type":"journal-article","created":{"date-parts":[[2016,1,2]],"date-time":"2016-01-02T15:23:24Z","timestamp":1451748204000},"page":"1057-1078","source":"Crossref","is-referenced-by-count":13,"title":["Set Estimation from Reflected Brownian Motion"],"prefix":"10.1093","volume":"78","author":[{"given":"Alejandro","family":"Cholaquidis","sequence":"first","affiliation":[{"name":"Universidad de la Rep\u00fablica , Montevideo , Uruguay"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricardo","family":"Fraiman","sequence":"additional","affiliation":[{"name":"Universidad de la Rep\u00fablica , Montevideo , Uruguay"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00e1bor","family":"Lugosi","sequence":"additional","affiliation":[{"name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats and Universitat Pompeu Fabra , Barcelona , Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Beatriz","family":"Pateiro-L\u00f3pez","sequence":"additional","affiliation":[{"name":"Universidad de Santiago de Compostela \u00a0 Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2016,1,1]]},"reference":[{"key":"2023021709301881700_rssb12149-cit-0001","doi-asserted-by":"crossref","first-page":"765","DOI":"10.2307\/3315915","article-title":"Set estimation and nonparametric detection","volume":"28","author":"Ba\u00edllo","year":"2000","journal-title":"Can. 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