{"id":"https://openalex.org/W2799278752","doi":"https://doi.org/10.1109/lsp.2018.2831178","title":"On the Maximum Likelihood Estimator Statistics for Unimodal Elliptical Distributions in the High Signal-to-Noise Ratio Regime","display_name":"On the Maximum Likelihood Estimator Statistics for Unimodal Elliptical Distributions in the High Signal-to-Noise Ratio Regime","publication_year":2018,"publication_date":"2018-04-27","ids":{"openalex":"https://openalex.org/W2799278752","doi":"https://doi.org/10.1109/lsp.2018.2831178","mag":"2799278752"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2018.2831178","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2018.2831178","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,"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"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01798888","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090329151","display_name":"Steeve Zozor","orcid":"https://orcid.org/0000-0001-7595-9601"},"institutions":[{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Steeve Zozor","raw_affiliation_strings":["Image and Signal Processing Department, GIPSA-Lab, Saint-Martin-d\u2019Hres, France","GIPSA-CICS - GIPSA - Communication Information and Complex Systems (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Image and Signal Processing Department, GIPSA-Lab, Saint-Martin-d\u2019Hres, France","institution_ids":["https://openalex.org/I4210124956"]},{"raw_affiliation_string":"GIPSA-CICS - GIPSA - Communication Information and Complex Systems (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)","institution_ids":["https://openalex.org/I4210124956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029566720","display_name":"Chengfang Ren","orcid":"https://orcid.org/0000-0001-8438-4539"},"institutions":[{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Chengfang Ren","raw_affiliation_strings":["SONDRA, CentraleSup\u00e9lec, Gif-sur-Yvette, France","SONDRA - Sondra, CentraleSup\u00e9lec, Universit\u00e9 Paris-Saclay (COmUE) (F- 91190 Gif-sur-Yvette - France)"],"affiliations":[{"raw_affiliation_string":"SONDRA, CentraleSup\u00e9lec, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"SONDRA - Sondra, CentraleSup\u00e9lec, Universit\u00e9 Paris-Saclay (COmUE) (F- 91190 Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I4210107720","https://openalex.org/I277688954"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044736586","display_name":"Alexandre Renaux","orcid":"https://orcid.org/0000-0003-3413-1765"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Renaux","raw_affiliation_strings":["LSS Universit\u00e9 Paris-Sud, Gif-sur-Yvette, France","L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"LSS Universit\u00e9 Paris-Sud, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I277688954","https://openalex.org/I102197404"]},{"raw_affiliation_string":"L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210097418"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090329151"],"corresponding_institution_ids":["https://openalex.org/I4210124956"],"apc_list":null,"apc_paid":null,"fwci":0.5981,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7112823,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"6","first_page":"883","last_page":"887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9966999888420105,"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"}},"topics":[{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9966999888420105,"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/T11186","display_name":"Hydrology and Drought Analysis","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9890000224113464,"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/estimator","display_name":"Estimator","score":0.7558915615081787},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.693422257900238},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.6665616631507874},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.605196475982666},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5572820901870728},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5050771832466125},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4822733998298645},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.46185553073883057},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.431529700756073},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43065354228019714},{"id":"https://openalex.org/keywords/consistent-estimator","display_name":"Consistent estimator","score":0.4296188950538635},{"id":"https://openalex.org/keywords/elliptical-distribution","display_name":"Elliptical distribution","score":0.4207109212875366},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.34782934188842773},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.30341869592666626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27172625064849854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21952226758003235},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21215838193893433},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13799631595611572},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09557664394378662},{"id":"https://openalex.org/keywords/multivariate-normal-distribution","display_name":"Multivariate normal distribution","score":0.0605735182762146}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7558915615081787},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.693422257900238},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6665616631507874},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.605196475982666},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5572820901870728},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5050771832466125},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4822733998298645},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46185553073883057},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.431529700756073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43065354228019714},{"id":"https://openalex.org/C164172150","wikidata":"https://www.wikidata.org/wiki/Q1782585","display_name":"Consistent estimator","level":4,"score":0.4296188950538635},{"id":"https://openalex.org/C130545031","wikidata":"https://www.wikidata.org/wiki/Q5365806","display_name":"Elliptical distribution","level":4,"score":0.4207109212875366},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.34782934188842773},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.30341869592666626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27172625064849854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21952226758003235},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21215838193893433},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13799631595611572},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09557664394378662},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.0605735182762146},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2018.2831178","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2018.2831178","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,"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:HAL:hal-01798888v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01798888","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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, 2018, 25 (6), pp.883 - 887. ⟨10.1109/LSP.2018.2831178⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01798888v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01798888","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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, 2018, 25 (6), pp.883 - 887. ⟨10.1109/LSP.2018.2831178⟩","raw_type":"Journal articles"},"sustainable_development_goals":[{"score":0.6200000047683716,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W45374770","https://openalex.org/W620038288","https://openalex.org/W1795535613","https://openalex.org/W1982290653","https://openalex.org/W1992422870","https://openalex.org/W1998619312","https://openalex.org/W2001729062","https://openalex.org/W2020541544","https://openalex.org/W2022894179","https://openalex.org/W2028119257","https://openalex.org/W2061735246","https://openalex.org/W2075037028","https://openalex.org/W2082100828","https://openalex.org/W2099279775","https://openalex.org/W2105675447","https://openalex.org/W2107408144","https://openalex.org/W2111640869","https://openalex.org/W2111855076","https://openalex.org/W2112883107","https://openalex.org/W2113007636","https://openalex.org/W2113945798","https://openalex.org/W2116414176","https://openalex.org/W2122759946","https://openalex.org/W2125412367","https://openalex.org/W2134815375","https://openalex.org/W2142485381","https://openalex.org/W2145126087","https://openalex.org/W2151983721","https://openalex.org/W2165112171","https://openalex.org/W2167683733","https://openalex.org/W2737602765","https://openalex.org/W3099401462","https://openalex.org/W3150333624","https://openalex.org/W4246756383","https://openalex.org/W4300246981","https://openalex.org/W6675061968","https://openalex.org/W6680941772"],"related_works":["https://openalex.org/W2349547417","https://openalex.org/W2036696807","https://openalex.org/W2350206592","https://openalex.org/W1984619412","https://openalex.org/W2910434125","https://openalex.org/W3092888124","https://openalex.org/W4239491110","https://openalex.org/W2035998077","https://openalex.org/W2802667153","https://openalex.org/W2092213901"],"abstract_inverted_index":{"In":[0],"this":[1,56,74],"letter,":[2],"we":[3,89],"study":[4],"the":[5,8,14,25,37,41,45,52,62,70,84],"behavior":[6],"of":[7,16,55,69],"maximum":[9],"likelihood":[10],"estimator":[11,57,75],"(MLE)":[12],"in":[13,40,83],"framework":[15],"low":[17],"noise":[18,46,71,86],"level":[19],"(or":[20],"high":[21],"signal-to-noise":[22],"ratio),":[23],"when":[24],"data":[26],"follow":[27],"a":[28],"unimodal":[29,59],"elliptical":[30],"distribution.":[31,47,72],"The":[32],"MLE":[33],"appears":[34],"to":[35,67,78],"be":[36,79],"same":[38],"as":[39],"Gaussian":[42,85],"context,":[43],"regardless":[44],"We":[48],"also":[49],"show":[50],"that":[51,68],"asymptotic":[53],"distribution":[54],"is":[58,64,76],"elliptical,":[60],"where":[61],"law":[63],"intimately":[65],"linked":[66],"Additionally,":[73],"shown":[77],"not":[80],"efficient,":[81],"except":[82],"case.":[87],"Finally,":[88],"validate":[90],"our":[91],"analytic":[92],"results":[93],"by":[94],"some":[95],"simulations.":[96]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}