{"id":"https://openalex.org/W7130708694","doi":"https://doi.org/10.1007/s11222-026-10852-6","title":"Robust distances and multivariate outlier detection under heavy tails","display_name":"Robust distances and multivariate outlier detection under heavy tails","publication_year":2026,"publication_date":"2026-02-20","ids":{"openalex":"https://openalex.org/W7130708694","doi":"https://doi.org/10.1007/s11222-026-10852-6"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-026-10852-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-026-10852-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-026-10852-6.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/s11222-026-10852-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072980245","display_name":"Lucio Barabesi","orcid":"https://orcid.org/0000-0002-7210-4541"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lucio Barabesi","raw_affiliation_strings":["Department of Economics and Statistics, University of Siena, Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics and Statistics, University of Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077676878","display_name":"Andrea Cerioli","orcid":"https://orcid.org/0000-0002-2485-5674"},"institutions":[{"id":"https://openalex.org/I124601658","display_name":"University of Parma","ror":"https://ror.org/02k7wn190","country_code":"IT","type":"education","lineage":["https://openalex.org/I124601658"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Andrea Cerioli","raw_affiliation_strings":["Department of Economics and Management, University of Parma, Parma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics and Management, University of Parma, Parma, Italy","institution_ids":["https://openalex.org/I124601658"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056108169","display_name":"Luis \u00c1ngel Garc\u00eda-Escudero","orcid":"https://orcid.org/0000-0002-7617-3034"},"institutions":[{"id":"https://openalex.org/I108103353","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18","country_code":"ES","type":"education","lineage":["https://openalex.org/I108103353"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Luis Angel Garc\u00eda-Escudero","raw_affiliation_strings":["Department of Statistics and Operations Research, University of Valladolid, Valladolid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, University of Valladolid, Valladolid, Spain","institution_ids":["https://openalex.org/I108103353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069383879","display_name":"Agust\u00edn Mayo-\u00cdscar","orcid":"https://orcid.org/0000-0003-0951-6508"},"institutions":[{"id":"https://openalex.org/I108103353","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18","country_code":"ES","type":"education","lineage":["https://openalex.org/I108103353"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Agust\u00edn Mayo-Iscar","raw_affiliation_strings":["Department of Statistics and Operations Research, University of Valladolid, Valladolid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, University of Valladolid, Valladolid, Spain","institution_ids":["https://openalex.org/I108103353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064148555","display_name":"Domenico Perrotta","orcid":"https://orcid.org/0000-0002-0987-3823"},"institutions":[{"id":"https://openalex.org/I4210118689","display_name":"Joint Research Centre","ror":"https://ror.org/02qezmz13","country_code":"IT","type":"government","lineage":["https://openalex.org/I1320481043","https://openalex.org/I2800387288","https://openalex.org/I4210118689","https://openalex.org/I4210161702"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Domenico Perrotta","raw_affiliation_strings":["European Commission, Joint Research Centre (JRC), Ispra, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"European Commission, Joint Research Centre (JRC), Ispra, Italy","institution_ids":["https://openalex.org/I4210118689"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064050877","display_name":"Francesca Torti","orcid":"https://orcid.org/0000-0003-0801-1735"},"institutions":[{"id":"https://openalex.org/I4210118689","display_name":"Joint Research Centre","ror":"https://ror.org/02qezmz13","country_code":"IT","type":"government","lineage":["https://openalex.org/I1320481043","https://openalex.org/I2800387288","https://openalex.org/I4210118689","https://openalex.org/I4210161702"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesca Torti","raw_affiliation_strings":["European Commission, Joint Research Centre (JRC), Ispra, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"European Commission, Joint Research Centre (JRC), Ispra, Italy","institution_ids":["https://openalex.org/I4210118689"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5077676878"],"corresponding_institution_ids":["https://openalex.org/I124601658"],"apc_list":{"value":2090,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2090,"currency":"EUR","value_usd":2690},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29417106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","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":0.8138999938964844,"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":0.8138999938964844,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.0348999984562397,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.02500000037252903,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantile","display_name":"Quantile","score":0.7595000267028809},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.7279000282287598},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6549000144004822},{"id":"https://openalex.org/keywords/mahalanobis-distance","display_name":"Mahalanobis distance","score":0.6047999858856201},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6010000109672546},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.574999988079071},{"id":"https://openalex.org/keywords/robust-statistics","display_name":"Robust statistics","score":0.5264000296592712},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.43880000710487366}],"concepts":[{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.7595000267028809},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.7279000282287598},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6549000144004822},{"id":"https://openalex.org/C1921717","wikidata":"https://www.wikidata.org/wiki/Q1334846","display_name":"Mahalanobis distance","level":2,"score":0.6047999858856201},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6010000109672546},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C67226441","wikidata":"https://www.wikidata.org/wiki/Q1665389","display_name":"Robust statistics","level":3,"score":0.5264000296592712},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5001999735832214},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.43880000710487366},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4334000051021576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4300999939441681},{"id":"https://openalex.org/C739882","wikidata":"https://www.wikidata.org/wiki/Q3560506","display_name":"Anomaly detection","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.38989999890327454},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.37220001220703125},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34880000352859497},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.3264999985694885},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.32089999318122864},{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29350000619888306},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.2754000127315521},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C137668524","wikidata":"https://www.wikidata.org/wiki/Q189813","display_name":"Censoring (clinical trials)","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11222-026-10852-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-026-10852-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-026-10852-6.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"}],"best_oa_location":{"id":"doi:10.1007/s11222-026-10852-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-026-10852-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-026-10852-6.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":[{"display_name":"Peace, Justice and strong institutions","score":0.6471192240715027,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G7915277041","display_name":null,"funder_award_id":"2021-2027","funder_id":"https://openalex.org/F4320334322","funder_display_name":"HORIZON EUROPE Framework Programme"},{"id":"https://openalex.org/G8503085978","display_name":null,"funder_award_id":"2021-2027","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322875","display_name":"Universit\u00e0 degli Studi di Parma","ror":"https://ror.org/02k7wn190"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null},{"id":"https://openalex.org/F4320334701","display_name":"Joint Research Centre","ror":"https://ror.org/04j5wtv36"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W7130708694.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W269863884","https://openalex.org/W1987333632","https://openalex.org/W1991935923","https://openalex.org/W1993707319","https://openalex.org/W2017977879","https://openalex.org/W2019061583","https://openalex.org/W2033533776","https://openalex.org/W2037855816","https://openalex.org/W2083241629","https://openalex.org/W2084617519","https://openalex.org/W2111131733","https://openalex.org/W2133730794","https://openalex.org/W2137971377","https://openalex.org/W2155678318","https://openalex.org/W2161384143","https://openalex.org/W2498631646","https://openalex.org/W2757169940","https://openalex.org/W2914136759","https://openalex.org/W2991541219","https://openalex.org/W3197726986","https://openalex.org/W4221098248","https://openalex.org/W4240826949","https://openalex.org/W4376616461","https://openalex.org/W4387095339","https://openalex.org/W4387452548","https://openalex.org/W4387575377","https://openalex.org/W4390055447","https://openalex.org/W4392981561"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Heavy-tailed":[1],"distributions,":[2],"such":[3],"as":[4,13],"the":[5,33,43,91,97,102,106,119,131,135,153,164,168,174,191,202,209,217,220],"Student-":[6,87,155],"t":[7,88,156],"distribution,":[8,89],"have":[9],"long":[10],"been":[11],"advocated":[12],"\u201crobust\u201d":[14],"models":[15],"for":[16,149],"multivariate":[17,86,154],"data":[18,98],"in":[19],"many":[20],"fields.":[21],"The":[22,108],"underlying":[23],"rationale":[24],"is":[25,49,93,118],"that":[26,52,110],"robustness":[27],"should":[28],"be":[29],"achieved":[30],"by":[31],"letting":[32],"classical":[34],"maximum-likelihood":[35],"estimators":[36],"accommodate":[37],"extreme":[38],"observations":[39],"naturally":[40],"arising":[41],"from":[42],"process":[44,100],"under":[45,57,82],"investigation.":[46],"However,":[47],"there":[48],"growing":[50],"recognition":[51],"contamination":[53,83,175],"might":[54],"also":[55],"occur":[56],"non-Gaussian":[58],"scenarios.":[59],"In":[60,125],"this":[61,126],"work":[62],"we":[63,128,180,196,215],"develop":[64],"a":[65,85],"unified":[66,116],"approach":[67,117],"which":[68],"exploits":[69],"high-breakdown":[70],"estimation":[71,75,189],"to":[72,95,113,140,152,162,186],"ensure":[73],"robust":[74,141],"of":[76,84,101,105,121,134,167,170,173,190,201,204,211,219],"location,":[77],"scatter":[78],"and":[79,158,172,195,214],"tail":[80],"parameters":[81],"when":[90],"latter":[92],"assumed":[94],"rule":[96],"generating":[99],"uncontaminated":[103],"part":[104],"data.":[107],"framework":[109],"allows":[111],"us":[112],"achieve":[114],"our":[115,178,205,212],"theory":[120],"generalized":[122],"radius":[123],"processes.":[124],"framework,":[127],"first":[129],"obtain":[130],"influence":[132],"function":[133],"main":[136],"statistical":[137],"functionals":[138],"associated":[139,185],"Mahalanobis":[142],"distances.":[143],"We":[144,207],"then":[145],"suggest":[146],"new":[147],"statistics":[148],"measuring":[150],"conformance":[151],"distribution":[157],"an":[159],"automatic":[160],"procedure":[161],"infer":[163],"true":[165],"values":[166],"degrees":[169],"freedom":[171],"rate.":[176],"Along":[177],"path,":[179],"tackle":[181],"several":[182],"computational":[183],"challenges":[184],"Monte":[187],"Carlo":[188],"required":[192],"radius-process":[193],"quantiles":[194],"provide":[197,216],"extensive":[198],"simulation":[199],"evidence":[200],"accuracy":[203],"method.":[206],"guarantee":[208],"replicability":[210],"results":[213],"implementation":[218],"suggested":[221],"algorithms.":[222]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-02-21T00:00:00"}
