{"id":"https://openalex.org/W2969821512","doi":"https://doi.org/10.1109/tsp.2019.2932877","title":"On the Asymptotics of Maronna's Robust PCA","display_name":"On the Asymptotics of Maronna's Robust PCA","publication_year":2019,"publication_date":"2019-08-22","ids":{"openalex":"https://openalex.org/W2969821512","doi":"https://doi.org/10.1109/tsp.2019.2932877","mag":"2969821512"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2019.2932877","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2932877","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/1811.02069","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045998619","display_name":"Gordana Dra\u0161kovi\u0107","orcid":"https://orcid.org/0000-0002-2784-8234"},"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/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/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/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gordana Draskovic","raw_affiliation_strings":["L2S, CentraleSup\u00e9lec, CNRS, Universit\u00e9 Paris-Sud, 3 rue Joliot-Curie, Gif-sur-Yvette Cedex, France","Laboratoire des signaux et syst\u00e8mes"],"raw_orcid":"https://orcid.org/0000-0002-2784-8234","affiliations":[{"raw_affiliation_string":"L2S, CentraleSup\u00e9lec, CNRS, Universit\u00e9 Paris-Sud, 3 rue Joliot-Curie, Gif-sur-Yvette Cedex, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I4210107720"]},{"raw_affiliation_string":"Laboratoire des signaux et syst\u00e8mes","institution_ids":["https://openalex.org/I4210097418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059566872","display_name":"Arnaud Breloy","orcid":"https://orcid.org/0000-0002-3802-9015"},"institutions":[{"id":"https://openalex.org/I40434647","display_name":"Universit\u00e9 Paris Nanterre","ror":"https://ror.org/013bkhk48","country_code":"FR","type":"education","lineage":["https://openalex.org/I40434647"]},{"id":"https://openalex.org/I4387152587","display_name":"Laboratoire \u00e9nerg\u00e9tique m\u00e9canique \u00e9lectromagn\u00e9tisme","ror":"https://ror.org/00ae7xs76","country_code":"FR","type":"facility","lineage":["https://openalex.org/I40434647","https://openalex.org/I4387152587"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Arnaud Breloy","raw_affiliation_strings":["LEME\u2013EA4416, University Paris-Nanterrre, Nanterre, France","Laboratoire Energ\u00e9tique M\u00e9canique Electromagn\u00e9tisme"],"raw_orcid":"https://orcid.org/0000-0002-3802-9015","affiliations":[{"raw_affiliation_string":"LEME\u2013EA4416, University Paris-Nanterrre, Nanterre, France","institution_ids":["https://openalex.org/I40434647"]},{"raw_affiliation_string":"Laboratoire Energ\u00e9tique M\u00e9canique Electromagn\u00e9tisme","institution_ids":["https://openalex.org/I4387152587"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089919393","display_name":"Fr\u00e9d\u00e9ric Pascal","orcid":"https://orcid.org/0000-0003-0196-6395"},"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/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/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/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Frederic Pascal","raw_affiliation_strings":["L2S, CentraleSup\u00e9lec, CNRS, Universit\u00e9 Paris-Sud, 3 rue Joliot-Curie, Gif-sur-Yvette Cedex, France","CentraleSup\u00e9lec","Laboratoire des signaux et syst\u00e8mes"],"raw_orcid":"https://orcid.org/0000-0003-0196-6395","affiliations":[{"raw_affiliation_string":"L2S, CentraleSup\u00e9lec, CNRS, Universit\u00e9 Paris-Sud, 3 rue Joliot-Curie, Gif-sur-Yvette Cedex, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I4210107720"]},{"raw_affiliation_string":"CentraleSup\u00e9lec","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"Laboratoire des signaux et syst\u00e8mes","institution_ids":["https://openalex.org/I4210097418"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6252,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.70156642,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"67","issue":"19","first_page":"4964","last_page":"4975"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9983999729156494,"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":0.9983999729156494,"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9955999851226807,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9932000041007996,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7349990606307983},{"id":"https://openalex.org/keywords/wishart-distribution","display_name":"Wishart distribution","score":0.6557515859603882},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5925061106681824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5766956210136414},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5506375432014465},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5365991592407227},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4663464426994324},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46361854672431946},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4521957337856293},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.44617563486099243},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35712578892707825},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34574419260025024},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11597564816474915}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7349990606307983},{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.6557515859603882},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5925061106681824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5766956210136414},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5506375432014465},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5365991592407227},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4663464426994324},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46361854672431946},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4521957337856293},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.44617563486099243},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35712578892707825},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34574419260025024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11597564816474915},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2019.2932877","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2932877","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:1811.02069","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.02069","pdf_url":"https://arxiv.org/pdf/1811.02069","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,"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-02399630v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02399630","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 Transactions on Signal Processing, 2019, 67 (19), pp.4964-4975. ⟨10.1109/TSP.2019.2932877⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1811.02069","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.02069","pdf_url":"https://arxiv.org/pdf/1811.02069","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,"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":[],"awards":[{"id":"https://openalex.org/G3974623063","display_name":"Mondes num\u00e9riques: Donn\u00e9es, programmes et architectures distribu\u00e9s","funder_award_id":"ANR-11-LABX-0045","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5027824404","display_name":"Modern Adaptive Radar: Great Advances in Robust and Inference Techniques and Application","funder_award_id":"ANR-17-ASTR-0015","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1502461990","https://openalex.org/W1814500939","https://openalex.org/W1972206072","https://openalex.org/W1979573625","https://openalex.org/W1983104971","https://openalex.org/W1984614739","https://openalex.org/W1989174971","https://openalex.org/W1992511687","https://openalex.org/W1995201905","https://openalex.org/W1995956281","https://openalex.org/W2008418230","https://openalex.org/W2014509644","https://openalex.org/W2021137021","https://openalex.org/W2022449570","https://openalex.org/W2032978955","https://openalex.org/W2034646922","https://openalex.org/W2044822299","https://openalex.org/W2055894834","https://openalex.org/W2062052013","https://openalex.org/W2078966899","https://openalex.org/W2096229075","https://openalex.org/W2113274816","https://openalex.org/W2119959491","https://openalex.org/W2126568557","https://openalex.org/W2131570846","https://openalex.org/W2132158100","https://openalex.org/W2142485381","https://openalex.org/W2142635246","https://openalex.org/W2143045817","https://openalex.org/W2144110078","https://openalex.org/W2161503240","https://openalex.org/W2246214216","https://openalex.org/W2527523124","https://openalex.org/W2553806353","https://openalex.org/W2594922456","https://openalex.org/W2623952261","https://openalex.org/W2765209993","https://openalex.org/W2809185615","https://openalex.org/W2903931732","https://openalex.org/W2943006550","https://openalex.org/W3023218716","https://openalex.org/W4255282992","https://openalex.org/W4297757075","https://openalex.org/W6679359823","https://openalex.org/W6684391177","https://openalex.org/W6745355765"],"related_works":["https://openalex.org/W2146312983","https://openalex.org/W2389605595","https://openalex.org/W1586339758","https://openalex.org/W3131856045","https://openalex.org/W2364482911","https://openalex.org/W3134381438","https://openalex.org/W2057690963","https://openalex.org/W2118598748","https://openalex.org/W2011956837","https://openalex.org/W2108933226"],"abstract_inverted_index":{"The":[0],"eigenvalue":[1],"decomposition":[2],"(EVD)":[3],"parameters":[4,58,101],"of":[5,21,24,46,65,70,102,132,139],"the":[6,19,22,25,44,56,68,87,92,99,113,130,137,155],"second":[7,110],"order":[8],"statistics":[9],"are":[10],"ubiquitous":[11],"in":[12,67,91],"statistical":[13],"analysis":[14],"and":[15,62,149],"signal":[16],"processing.":[17],"Notably,":[18],"EVD":[20,57,100,131,138],"M-estimators":[23,66],"scatter":[26],"matrix":[27,90,134],"is":[28,80,107],"a":[29,103],"popular":[30],"choice":[31],"to":[32,123],"perform":[33],"robust":[34],"probabilistic":[35],"PCA":[36],"or":[37],"other":[38],"dimension":[39],"reduction":[40],"related":[41],"applications.":[42],"Towards":[43],"goal":[45],"characterizing":[47,136],"this":[48,50],"process,":[49],"paper":[51],"derives":[52],"new":[53],"asymptotics":[54],"for":[55,135],"(i.e.":[59],"eigenvalues,":[60],"eigenvectors,":[61],"principal":[63],"subspace)":[64],"context":[69],"complex":[71],"elliptically":[72],"symmetric":[73],"distributions.":[74],"First,":[75],"their":[76,96],"Gaussian":[77,93],"asymptotic":[78],"distribution":[79],"obtained":[81,156],"by":[82],"extending":[83],"standard":[84],"results":[85,128,157],"on":[86,126,129],"sample":[88],"covariance":[89],"context.":[94],"Second,":[95],"convergence":[97],"towards":[98],"Gaussian-Core":[104],"Wishart":[105],"Equivalent":[106],"derived.":[108],"This":[109],"result":[111],"represents":[112],"main":[114],"contributioninthe":[115],"sense":[116],"that":[117],"it":[118],"quantifies":[119],"when":[120],"itis":[121],"acceptable":[122],"directly":[124],"rely":[125],"well-established":[127],"Wishartdistributed":[133],"M-estimators.":[140],"Finally,":[141],"some":[142],"examples":[143],"(intrinsic":[144],"bias":[145],"analysis,":[146],"rank":[147],"estimation,":[148],"low-rank":[150],"adaptive":[151],"filtering)":[152],"illustrate":[153],"where":[154],"can":[158],"be":[159],"leveraged.":[160]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}