{"id":"https://openalex.org/W3184186548","doi":"https://doi.org/10.1007/s11222-023-10216-4","title":"Statistical depth in abstract metric spaces","display_name":"Statistical depth in abstract metric spaces","publication_year":2023,"publication_date":"2023-02-23","ids":{"openalex":"https://openalex.org/W3184186548","doi":"https://doi.org/10.1007/s11222-023-10216-4","mag":"3184186548"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-023-10216-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-023-10216-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-023-10216-4.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11222-023-10216-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037753859","display_name":"Gery Geenens","orcid":"https://orcid.org/0000-0003-1355-2659"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Gery Geenens","raw_affiliation_strings":["School of Mathematics and Statistics, UNSW Sydney, Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, UNSW Sydney, Sydney, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039890118","display_name":"Alicia Nieto-Reyes","orcid":"https://orcid.org/0000-0002-0268-3322"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alicia Nieto-Reyes","raw_affiliation_strings":["Department of Mathematics, Statistics and Computer Science, University of Cantabria, Santanders, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics and Computer Science, University of Cantabria, Santanders, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051450474","display_name":"Giacomo Francisci","orcid":null},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]},{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES","US"],"is_corresponding":false,"raw_author_name":"Giacomo Francisci","raw_affiliation_strings":["Department of Mathematics, Statistics and Computer Science, University of Cantabria, Santanders, Spain","Department of Statistics, George Mason University, Fairfax, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics and Computer Science, University of Cantabria, Santanders, Spain","institution_ids":["https://openalex.org/I13134134"]},{"raw_affiliation_string":"Department of Statistics, George Mason University, Fairfax, USA","institution_ids":["https://openalex.org/I162714631"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037753859"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":{"value":2090,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2090,"currency":"EUR","value_usd":2690},"fwci":3.8431,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.93999689,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"33","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.9783999919891357,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13141","display_name":"Statistical Methods and Applications","score":0.9445000290870667,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7075968980789185},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5930841565132141},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5651883482933044},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5415703058242798},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5380913615226746},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5190061330795288},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.5189823508262634},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48633986711502075},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4856204092502594},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.4816107451915741},{"id":"https://openalex.org/keywords/big-data","display_name":"Big data","score":0.4589240849018097},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43587526679039},{"id":"https://openalex.org/keywords/function-space","display_name":"Function space","score":0.4246104955673218},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3896182179450989},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3742554187774658},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.347015917301178},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17262333631515503},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14619958400726318},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07193785905838013}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7075968980789185},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5930841565132141},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5651883482933044},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5415703058242798},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5380913615226746},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5190061330795288},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.5189823508262634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48633986711502075},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4856204092502594},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.4816107451915741},{"id":"https://openalex.org/C75684735","wikidata":"https://www.wikidata.org/wiki/Q858810","display_name":"Big data","level":2,"score":0.4589240849018097},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43587526679039},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.4246104955673218},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3896182179450989},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3742554187774658},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.347015917301178},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17262333631515503},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14619958400726318},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07193785905838013},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11222-023-10216-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-023-10216-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-023-10216-4.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},{"id":"pmh:oai:repositorio.unican.es:10902/32315","is_oa":true,"landing_page_url":"https://hdl.handle.net/10902/32315","pdf_url":"https://repositorio.unican.es/xmlui/bitstream/10902/32315/3/StatisticalDepthAbstract.pdf","source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Statistics and Computing, 2023, 33(2), 46","raw_type":"publishedVersion"},{"id":"pmh:oai:iris.unitn.it:11572/470944","is_oa":false,"landing_page_url":"https://hdl.handle.net/11572/470944","pdf_url":null,"source":{"id":"https://openalex.org/S4306401913","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11222-023-10216-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-023-10216-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-023-10216-4.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5780362222","display_name":null,"funder_award_id":"MTM2017-86061-C2-2-P","funder_id":"https://openalex.org/F4320323896","funder_display_name":"Ministerio de Ciencia Tecnolog\u00eda y Telecomunicaciones"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320320965","display_name":"University of New South Wales","ror":"https://ror.org/03r8z3t63"},{"id":"https://openalex.org/F4320323896","display_name":"Ministerio de Ciencia Tecnolog\u00eda y Telecomunicaciones","ror":"https://ror.org/05dbsyw70"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3184186548.pdf"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W177959696","https://openalex.org/W418680382","https://openalex.org/W619520426","https://openalex.org/W1482555119","https://openalex.org/W1490292573","https://openalex.org/W1576898078","https://openalex.org/W1578430072","https://openalex.org/W1965995153","https://openalex.org/W1968300239","https://openalex.org/W1973744648","https://openalex.org/W1982141888","https://openalex.org/W1983326505","https://openalex.org/W1991163937","https://openalex.org/W1994166982","https://openalex.org/W2016312261","https://openalex.org/W2016440615","https://openalex.org/W2022291755","https://openalex.org/W2029061484","https://openalex.org/W2042809187","https://openalex.org/W2060504630","https://openalex.org/W2061318454","https://openalex.org/W2064101017","https://openalex.org/W2067707835","https://openalex.org/W2068044076","https://openalex.org/W2072242542","https://openalex.org/W2074532128","https://openalex.org/W2077260392","https://openalex.org/W2079815272","https://openalex.org/W2082299385","https://openalex.org/W2085570173","https://openalex.org/W2096814239","https://openalex.org/W2141055931","https://openalex.org/W2147618390","https://openalex.org/W2154999648","https://openalex.org/W2276499310","https://openalex.org/W2325183536","https://openalex.org/W2467389505","https://openalex.org/W2489577344","https://openalex.org/W2573121065","https://openalex.org/W2575909900","https://openalex.org/W2761490427","https://openalex.org/W2963374513","https://openalex.org/W2964259247","https://openalex.org/W2972122392","https://openalex.org/W3010758268","https://openalex.org/W3081886688","https://openalex.org/W3104502292","https://openalex.org/W3109595434","https://openalex.org/W3134271985","https://openalex.org/W3137136951","https://openalex.org/W3145149967","https://openalex.org/W3152764882","https://openalex.org/W4200343539","https://openalex.org/W4205462863","https://openalex.org/W4232667913","https://openalex.org/W4234079402","https://openalex.org/W4235500030","https://openalex.org/W4242534643","https://openalex.org/W4251011993","https://openalex.org/W4256540010","https://openalex.org/W4292156489","https://openalex.org/W4300633279"],"related_works":["https://openalex.org/W4390608645","https://openalex.org/W4247566972","https://openalex.org/W2960264696","https://openalex.org/W3090563135","https://openalex.org/W2497432351","https://openalex.org/W4206777497","https://openalex.org/W51364034","https://openalex.org/W2898073868","https://openalex.org/W4284663758","https://openalex.org/W4297851895"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"concept":[2,55],"of":[3,25,27,42,48,96,107],"depth":[4,63,72,82],"has":[5],"proved":[6],"very":[7,100],"important":[8],"for":[9,22],"multivariate":[10],"and":[11,65,91],"functional":[12],"data":[13,88,109,119],"analysis,":[14,98],"as":[15,19,69],"it":[16],"essentially":[17],"acts":[18],"a":[20,61,70,76,99],"surrogate":[21],"the":[23,39,46,81,87,93,97,104],"notion":[24],"ranking":[26],"observations":[28],"which":[29],"is":[30,113],"absent":[31],"in":[32,44,75],"more":[33],"than":[34],"one":[35],"dimension.":[36],"Motivated":[37],"by":[38,116],"rapid":[40],"development":[41],"technology,":[43],"particular":[45],"advent":[47],"\u2018Big":[49],"Data\u2019,":[50],"we":[51],"extend":[52],"here":[53],"that":[54],"to":[56,83,86,92],"general":[57,77],"metric":[58,78],"spaces,":[59],"propose":[60],"natural":[62],"measure":[64],"explore":[66],"its":[67],"properties":[68],"statistical":[71],"function.":[73],"Working":[74],"space":[79],"allows":[80],"be":[84],"tailored":[85],"at":[89],"hand":[90],"ultimate":[94],"goal":[95],"desirable":[101],"property":[102],"given":[103],"polymorphic":[105],"nature":[106],"modern":[108],"sets.":[110],"This":[111],"flexibility":[112],"thoroughly":[114],"illustrated":[115],"several":[117],"real":[118],"analyses.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}