{"corpus_id":17546613,"paper_sha":"917874c6b18eb02e19015572111ea301035d1901","doi":"10.5705/SS.2011.206","arxiv_id":"1109.4962","pmid":null,"pmcid":null,"mag_id":2952330702,"dblp_id":null,"acl_id":null,"title":"Optimal R-estimation of a spherical location","year":2011,"publication_date":"2011-09-22","venue":"","journal":{"name":"Statistica Sinica","pages":"305-332","volume":"23"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":30,"citation_count":35,"influential_citation_count":0,"is_open_access":true,"arxiv_categories":["stat.AP"],"arxiv_license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"http://arxiv.org/pdf/1109.4962","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/917874c6b18eb02e19015572111ea301035d1901","s2_open_access_license":null,"s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"In this paper, we provide R-estimators of the location of a rotationally symmetric distribution on the unit sphere of R k . In order to do so we first prove the local asymptotic normality property of a sequence of rotationally symmetric models; this is a non-standard result due to the curved nature of the unit sphere. We then construct our estimators by adapting the Le Cam one-step methodology to spherical statistics and ranks. We show that they are asymptotically normal under any rotationally symmetric distribution and achieve the efficiency bound under a specific density. Their small sample behavior is studied via a Monte Carlo simulation and our methodology is illustrated on geological data.","claims":[{"public_id":"cl_309f3e0bbab3bd95df94701f030164b9","status":"active","text":"R-estimators for the location of a rotationally symmetric distribution on the unit sphere are constructed by adapting the Le Cam one-step methodology to spherical statistics and ranks.","confidence":0.97,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_309f3e0bbab3bd95df94701f030164b9"},{"public_id":"cl_2acecb6806c81f42efcc2e80736f5ccc","status":"active","text":"Small-sample behavior is assessed through Monte Carlo simulation and the approach is illustrated on geological data.","confidence":0.9,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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