{"id":"https://openalex.org/W2105675447","doi":"https://doi.org/10.1109/lsp.2013.2281914","title":"On the Fisher Information Matrix for Multivariate Elliptically Contoured Distributions","display_name":"On the Fisher Information Matrix for Multivariate Elliptically Contoured Distributions","publication_year":2013,"publication_date":"2013-09-16","ids":{"openalex":"https://openalex.org/W2105675447","doi":"https://doi.org/10.1109/lsp.2013.2281914","mag":"2105675447"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2013.2281914","doi":"https://doi.org/10.1109/lsp.2013.2281914","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2013.2281914","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1306.6415","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040395588","display_name":"Olivier Besson","orcid":"https://orcid.org/0000-0001-6079-8446","observed_orcids":["https://orcid.org/0000-0001-6079-8446"]},"institutions":[{"id":"https://openalex.org/I4405258862","display_name":"Universit\u00e9 de Toulouse","ror":"https://ror.org/01ahyrz84","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Olivier Besson","raw_affiliation_strings":["ISAE, Department Electronics Optronics Signal, University of Toulouse, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ISAE, Department Electronics Optronics Signal, University of Toulouse, Toulouse, France","institution_ids":["https://openalex.org/I4405258862"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112005763","display_name":"Yuri I. Abramovich","orcid":"https://orcid.org/0000-0003-1563-3698","observed_orcids":["https://orcid.org/0000-0003-1563-3698"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuri I. Abramovich","raw_affiliation_strings":["WR Systems Limited, Fairfax, VA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"WR Systems Limited, Fairfax, VA, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":3.6393,"has_fulltext":true,"cited_by_count":81,"citation_normalized_percentile":{"value":0.95167376,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"20","issue":"11","first_page":"1130","last_page":"1133"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.44040000438690186,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.44040000438690186,"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.08799999952316284,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.07349999994039536,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fisher-information-matrix","display_name":"Fisher information matrix","score":1.0},{"id":"https://openalex.org/keywords/elliptically-contoured-distributions","display_name":"elliptically contoured distributions","score":0.953000009059906},{"id":"https://openalex.org/keywords/closed-form-expressions","display_name":"closed-form expressions","score":0.8159999847412109},{"id":"https://openalex.org/keywords/student-s-t-distribution","display_name":"t-distribution","score":0.7459999918937683},{"id":"https://openalex.org/keywords/normal-distribution","display_name":"normal distribution","score":0.492000013589859},{"id":"https://openalex.org/keywords/multivariate-analysis","display_name":"multivariate analysis","score":0.4269999861717224}],"concepts":[{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.8234999775886536},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.7110000252723694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6805999875068665},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.5760999917984009},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.5310999751091003},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4742000102996826},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.4616999924182892},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4526999890804291},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4377000033855438},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.4088999927043915},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39340001344680786},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.39259999990463257},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3921000063419342},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.34549999237060547},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3255999982357025},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2842000126838684},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C4530962","wikidata":"https://www.wikidata.org/wiki/Q777407","display_name":"Closed-form expression","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.2578999996185303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.257099986076355},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.25429999828338623},{"id":"https://openalex.org/C102094743","wikidata":"https://www.wikidata.org/wiki/Q133871","display_name":"Normal distribution","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/lsp.2013.2281914","doi":"https://doi.org/10.1109/lsp.2013.2281914","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2013.2281914","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1306.6415","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1306.6415","pdf_url":"https://arxiv.org/pdf/1306.6415","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.398.8264","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.398.8264","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/86/70/12/PDF/Besson_9579.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00867012v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-00867012","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Processing Letters, 2013, vol. 20, pp. 1130-1133. &#x27E8;10.1109/LSP.2013.2281914&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1306.6415","doi":"https://doi.org/10.48550/arxiv.1306.6415","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1306.6415","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1306.6415","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1306.6415","pdf_url":"https://arxiv.org/pdf/1306.6415","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2105675447.pdf","grobid_xml":"https://content.openalex.org/works/W2105675447.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W250076511","https://openalex.org/W280712306","https://openalex.org/W568214519","https://openalex.org/W1485745263","https://openalex.org/W1545857503","https://openalex.org/W1965392255","https://openalex.org/W1965809243","https://openalex.org/W1965928820","https://openalex.org/W1984614739","https://openalex.org/W1986921156","https://openalex.org/W1992511687","https://openalex.org/W2008330147","https://openalex.org/W2008364482","https://openalex.org/W2008418230","https://openalex.org/W2021553162","https://openalex.org/W2026239436","https://openalex.org/W2033323366","https://openalex.org/W2061811442","https://openalex.org/W2076764958","https://openalex.org/W2081622708","https://openalex.org/W2090705694","https://openalex.org/W2106199973","https://openalex.org/W2136194954","https://openalex.org/W2142485381","https://openalex.org/W2147116730","https://openalex.org/W2161503240","https://openalex.org/W4235107052","https://openalex.org/W4242597235"],"related_works":["https://openalex.org/W6885064600","https://openalex.org/W2611939839","https://openalex.org/W7130824693","https://openalex.org/W2029863687","https://openalex.org/W7029276566","https://openalex.org/W2388356710","https://openalex.org/W1967662947","https://openalex.org/W4311769938","https://openalex.org/W3044370843","https://openalex.org/W2140854119"],"abstract_inverted_index":{"The":[0,19],"Slepian-Bangs":[1,110],"formula":[2,106,111],"provides":[3],"a":[4,29,43],"very":[5],"convenient":[6],"way":[7],"to":[8,25,28,108],"compute":[9],"the":[10,47,56,60,71,77,86,91,104,109,113],"Fisher":[11],"information":[12],"matrix":[13],"(FIM)":[14],"for":[15,82],"Gaussian":[16,61,95,114],"distributed":[17],"data.":[18],"aim":[20],"of":[21,32,46,59,73,76,90],"this":[22,50],"letter":[23],"is":[24],"extend":[26],"it":[27,127],"larger":[30],"family":[31],"distributions,":[33],"namely":[34],"elliptically":[35],"contoured":[36],"(EC)":[37],"distributions.":[38],"More":[39],"precisely,":[40],"we":[41,117],"derive":[42],"closed-form":[44],"expression":[45,54],"FIM":[48,62,92],"in":[49,85,112],"case.":[51],"This":[52],"new":[53,105],"involves":[55,97],"usual":[57],"term":[58],"plus":[63],"some":[64,74],"corrective":[65],"factors":[66],"that":[67,103],"depend":[68],"only":[69],"on":[70,125],"expectations":[72],"functions":[75],"so-called":[78],"modular":[79],"variate.":[80],"Hence,":[81],"most":[83],"distributions":[84,124],"EC":[87],"family,":[88],"derivation":[89],"from":[93],"its":[94],"counterpart":[96],"slight":[98],"additional":[99],"derivations.":[100],"We":[101],"show":[102],"reduces":[107],"case":[115],"and":[116],"provide":[118],"an":[119],"illustrative":[120],"example":[121],"with":[122],"Student":[123],"how":[126],"can":[128],"be":[129],"used.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
