{"id":"https://openalex.org/W1659823078","doi":"https://doi.org/10.1109/tsp.2015.2447493","title":"Estimation of Toeplitz Covariance Matrices in Large Dimensional Regime With Application to Source Detection","display_name":"Estimation of Toeplitz Covariance Matrices in Large Dimensional Regime With Application to Source Detection","publication_year":2015,"publication_date":"2015-06-19","ids":{"openalex":"https://openalex.org/W1659823078","doi":"https://doi.org/10.1109/tsp.2015.2447493","mag":"1659823078"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2015.2447493","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2447493","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1403.1243","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112145518","display_name":"Julia Vinogradova","orcid":null},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210165912","display_name":"Laboratoire Traitement et Communication de l\u2019Information","ror":"https://ror.org/057er4c39","country_code":"FR","type":"facility","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102","https://openalex.org/I4210165912"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Julia Vinogradova","raw_affiliation_strings":["CNRS LTCI, Telecom ParisTech, France","CNRS-LTCI, Telecom-ParisTech, France;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS LTCI, Telecom ParisTech, France","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I1294671590","https://openalex.org/I4210165912"]},{"raw_affiliation_string":"CNRS-LTCI, Telecom-ParisTech, France;","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I1294671590","https://openalex.org/I4210165912"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021257434","display_name":"Romain Couillet","orcid":"https://orcid.org/0000-0001-5755-2090"},"institutions":[{"id":"https://openalex.org/I102475099","display_name":"Sup\u00e9lec","ror":"https://ror.org/00n7gwn90","country_code":"FR","type":"education","lineage":["https://openalex.org/I102475099"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Romain Couillet","raw_affiliation_strings":["Supelec, France","Supel\u00e9c, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Supelec, France","institution_ids":["https://openalex.org/I102475099"]},{"raw_affiliation_string":"Supel\u00e9c, France","institution_ids":["https://openalex.org/I102475099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052471480","display_name":"Walid Hachem","orcid":"https://orcid.org/0000-0001-8499-2761"},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210165912","display_name":"Laboratoire Traitement et Communication de l\u2019Information","ror":"https://ror.org/057er4c39","country_code":"FR","type":"facility","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102","https://openalex.org/I4210165912"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Walid Hachem","raw_affiliation_strings":["CNRS LTCI, Telecom ParisTech, France","CNRS-LTCI, Telecom-ParisTech, France;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS LTCI, Telecom ParisTech, France","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I1294671590","https://openalex.org/I4210165912"]},{"raw_affiliation_string":"CNRS-LTCI, Telecom-ParisTech, France;","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I1294671590","https://openalex.org/I4210165912"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2255,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.87948503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"63","issue":"18","first_page":"4903","last_page":"4913"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9968000054359436,"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/T11716","display_name":"Random Matrices and Applications","score":0.9968000054359436,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9812999963760376,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9807000160217285,"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8158938884735107},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.6650316715240479},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6192947626113892},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.6069735884666443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6048211455345154},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5900834202766418},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5854208469390869},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5229442715644836},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4796631634235382},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.47631940245628357},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.444539338350296},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.43740314245224},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41490834951400757},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41453564167022705},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3543652296066284},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3317556381225586},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23333904147148132},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17677569389343262},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1621486246585846},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.16006705164909363},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08872157335281372}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8158938884735107},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.6650316715240479},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6192947626113892},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6069735884666443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6048211455345154},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5900834202766418},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5854208469390869},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5229442715644836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4796631634235382},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.47631940245628357},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.444539338350296},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.43740314245224},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41490834951400757},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41453564167022705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3543652296066284},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3317556381225586},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23333904147148132},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17677569389343262},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1621486246585846},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.16006705164909363},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08872157335281372},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2015.2447493","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2447493","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1403.1243","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1403.1243","pdf_url":"https://arxiv.org/pdf/1403.1243","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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:HAL:hal-01241741v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01241741","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Signal Processing, 2015, 63 (18), pp.4903 - 4913. ⟨10.1109/TSP.2015.2447493⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1403.1243","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1403.1243","pdf_url":"https://arxiv.org/pdf/1403.1243","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[{"score":0.5199999809265137,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1573820523","https://openalex.org/W1972276842","https://openalex.org/W2017170340","https://openalex.org/W2061303336","https://openalex.org/W2068135051","https://openalex.org/W2072207996","https://openalex.org/W2103482025","https://openalex.org/W2130351130","https://openalex.org/W2132105090","https://openalex.org/W2150307184","https://openalex.org/W3098365576","https://openalex.org/W3098880893","https://openalex.org/W3101788651","https://openalex.org/W3104169636","https://openalex.org/W4206196235","https://openalex.org/W4243833160","https://openalex.org/W4301084947"],"related_works":["https://openalex.org/W2353873167","https://openalex.org/W2921280830","https://openalex.org/W2126916073","https://openalex.org/W4291238690","https://openalex.org/W2131680714","https://openalex.org/W2887132723","https://openalex.org/W2170667396","https://openalex.org/W2886934452","https://openalex.org/W2024369332","https://openalex.org/W2028568336"],"abstract_inverted_index":{"In":[0],"this":[1,89],"paper,":[2],"we":[3],"derive":[4],"concentration":[5],"inequalities":[6],"for":[7],"the":[8,36,39,61,63,69,96],"spectral":[9],"norm":[10],"of":[11,16,42,60,65,71,103],"two":[12],"classical":[13],"sample":[14],"estimators":[15],"large":[17,72],"dimensional":[18,73],"Toeplitz":[19],"covariance":[20],"matrices,":[21],"demonstrating":[22],"in":[23,68],"particular":[24],"their":[25],"asymptotic":[26],"almost":[27],"sure":[28],"consistence.":[29],"The":[30],"consistency":[31],"is":[32,45,82,91],"then":[33],"extended":[34],"to":[35,86,98],"case":[37],"where":[38],"aggregated":[40],"matrix":[41],"time":[43],"samples":[44],"corrupted":[46],"by":[47],"a":[48,77,100],"rank":[49],"one":[50],"(or":[51],"more":[52],"generally,":[53],"low":[54],"rank)":[55],"matrix.":[56],"As":[57,84],"an":[58],"application":[59,90],"latter,":[62],"problem":[64],"source":[66],"detection":[67],"context":[70],"sensor":[74],"networks":[75],"within":[76],"temporally":[78],"correlated":[79],"noise":[80,105],"environment":[81],"studied.":[83],"opposed":[85],"standard":[87],"procedures,":[88],"performed":[92],"online,":[93],"i.e.,":[94],"without":[95],"need":[97],"possess":[99],"learning":[101],"set":[102],"pure":[104],"samples.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}