{"id":"https://openalex.org/W2107993500","doi":"https://doi.org/10.1109/tsp.2015.2474298","title":"A Robust Statistics Approach to Minimum Variance Portfolio Optimization","display_name":"A Robust Statistics Approach to Minimum Variance Portfolio Optimization","publication_year":2015,"publication_date":"2015-08-28","ids":{"openalex":"https://openalex.org/W2107993500","doi":"https://doi.org/10.1109/tsp.2015.2474298","mag":"2107993500"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2015.2474298","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2474298","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/1503.08013","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036598759","display_name":"Liusha Yang","orcid":"https://orcid.org/0000-0003-0176-5446"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liusha Yang","raw_affiliation_strings":["Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong","Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Kowloon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Kowloon","institution_ids":["https://openalex.org/I200769079"]}]},{"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/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/I102475099","display_name":"Sup\u00e9lec","ror":"https://ror.org/00n7gwn90","country_code":"FR","type":"education","lineage":["https://openalex.org/I102475099"]},{"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":"Romain Couillet","raw_affiliation_strings":["CNRS-CentraleSup\u00e9lec-Universit\u00e9 Paris-Sud, Laboratoire de Signaux et Systmes (L2S, UMR8506), Gif-sur-Yvette, France","Laboratoire de Signaux et Systmes (L2S, UMR8506), CNRS-CentraleSup\u00e9lec-Universit\u00e9 Paris-Sud, Gif-sur-Yvette, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS-CentraleSup\u00e9lec-Universit\u00e9 Paris-Sud, Laboratoire de Signaux et Systmes (L2S, UMR8506), Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I102475099","https://openalex.org/I1294671590","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"raw_affiliation_string":"Laboratoire de Signaux et Systmes (L2S, UMR8506), CNRS-CentraleSup\u00e9lec-Universit\u00e9 Paris-Sud, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091126453","display_name":"Matthew R. McKay","orcid":"https://orcid.org/0000-0002-8086-2545"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Matthew R. McKay","raw_affiliation_strings":["Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong","Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Kowloon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Kowloon","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.1595,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.96992774,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"63","issue":"24","first_page":"6684","last_page":"6697"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9995999932289124,"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":0.9995999932289124,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9952999949455261,"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/portfolio-optimization","display_name":"Portfolio optimization","score":0.8356916308403015},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.708337664604187},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.6167424321174622},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6136642098426819},{"id":"https://openalex.org/keywords/modern-portfolio-theory","display_name":"Modern portfolio theory","score":0.5796443819999695},{"id":"https://openalex.org/keywords/shrinkage-estimator","display_name":"Shrinkage estimator","score":0.5576333403587341},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.5506314039230347},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.5220006704330444},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49148499965667725},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.49054068326950073},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.46347153186798096},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45594534277915955},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.4489433765411377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41057348251342773},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34785833954811096},{"id":"https://openalex.org/keywords/bias-of-an-estimator","display_name":"Bias of an estimator","score":0.22750088572502136},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.17239826917648315},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.1330547332763672}],"concepts":[{"id":"https://openalex.org/C202655437","wikidata":"https://www.wikidata.org/wiki/Q7231728","display_name":"Portfolio optimization","level":3,"score":0.8356916308403015},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.708337664604187},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.6167424321174622},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6136642098426819},{"id":"https://openalex.org/C9725762","wikidata":"https://www.wikidata.org/wiki/Q1072885","display_name":"Modern portfolio theory","level":3,"score":0.5796443819999695},{"id":"https://openalex.org/C102592046","wikidata":"https://www.wikidata.org/wiki/Q7504144","display_name":"Shrinkage estimator","level":5,"score":0.5576333403587341},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.5506314039230347},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.5220006704330444},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49148499965667725},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.49054068326950073},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.46347153186798096},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45594534277915955},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4489433765411377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41057348251342773},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34785833954811096},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.22750088572502136},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.17239826917648315},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.1330547332763672}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2015.2474298","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2474298","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:1503.08013","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.08013","pdf_url":"https://arxiv.org/pdf/1503.08013","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-01262628v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01262628","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 (24), pp.6684 - 6697. &#x27E8;10.1109/TSP.2015.2474298&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1503.08013","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.08013","pdf_url":"https://arxiv.org/pdf/1503.08013","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W1548938959","https://openalex.org/W1586554030","https://openalex.org/W1632651649","https://openalex.org/W1812558952","https://openalex.org/W1813708725","https://openalex.org/W1829169350","https://openalex.org/W1965928820","https://openalex.org/W1970686657","https://openalex.org/W1971523416","https://openalex.org/W1974640819","https://openalex.org/W1979573625","https://openalex.org/W1984038545","https://openalex.org/W1989576509","https://openalex.org/W2008418230","https://openalex.org/W2017052897","https://openalex.org/W2017808917","https://openalex.org/W2021614726","https://openalex.org/W2026239436","https://openalex.org/W2033715518","https://openalex.org/W2046033161","https://openalex.org/W2052364013","https://openalex.org/W2062125287","https://openalex.org/W2066680775","https://openalex.org/W2073681337","https://openalex.org/W2076396344","https://openalex.org/W2084478869","https://openalex.org/W2091786408","https://openalex.org/W2093432936","https://openalex.org/W2097517131","https://openalex.org/W2100011707","https://openalex.org/W2108823152","https://openalex.org/W2115972246","https://openalex.org/W2127000676","https://openalex.org/W2132158100","https://openalex.org/W2134056163","https://openalex.org/W2135395072","https://openalex.org/W2143045817","https://openalex.org/W2144809865","https://openalex.org/W2147116730","https://openalex.org/W2147675445","https://openalex.org/W2163969674","https://openalex.org/W2164883547","https://openalex.org/W2165408259","https://openalex.org/W2891149505","https://openalex.org/W2951144730","https://openalex.org/W3104963122","https://openalex.org/W3105672394","https://openalex.org/W3121324299","https://openalex.org/W3121451334","https://openalex.org/W3121764760","https://openalex.org/W3122301309","https://openalex.org/W3123792221","https://openalex.org/W3126088862","https://openalex.org/W3151203283","https://openalex.org/W4236670843","https://openalex.org/W4249736682","https://openalex.org/W4255103909","https://openalex.org/W4299657353","https://openalex.org/W4300916061"],"related_works":["https://openalex.org/W3198789915","https://openalex.org/W2342245948","https://openalex.org/W2113583687","https://openalex.org/W2396009620","https://openalex.org/W3141254748","https://openalex.org/W4387811153","https://openalex.org/W1589314636","https://openalex.org/W2498125471","https://openalex.org/W4312259442","https://openalex.org/W2489358856"],"abstract_inverted_index":{"We":[0,80],"study":[1],"the":[2,14,19,22,27,34,46,52,77,86,127,137],"design":[3],"of":[4,13,21,26,36,42,48,88,122],"portfolios":[5],"under":[6],"a":[7,59,89,119],"minimum":[8],"risk":[9],"criterion.":[10],"The":[11],"performance":[12,87],"optimized":[15],"portfolio":[16,28,129,141],"relies":[17],"on":[18,95,100],"accuracy":[20],"estimated":[23],"covariance":[24,54,60,78,91],"matrix":[25,55,92,115],"asset":[29],"returns.":[30],"For":[31],"large":[32],"portfolios,":[33],"number":[35,47],"available":[37],"market":[38,64,157],"returns":[39],"is":[40,132,144],"often":[41,66],"similar":[43],"order":[44],"to":[45,148],"assets,":[49],"so":[50],"that":[51],"sample":[53],"performs":[56],"poorly":[57],"as":[58],"estimator.":[61],"Additionally,":[62],"financial":[63],"data":[65],"contain":[67],"outliers":[68],"which,":[69],"if":[70],"not":[71],"correctly":[72],"handled,":[73],"may":[74],"further":[75],"corrupt":[76],"estimation.":[79],"address":[81],"these":[82],"shortcomings":[83],"by":[84,134],"studying":[85],"hybrid":[90],"estimator":[93,103,121],"based":[94],"Tyler's":[96],"robust":[97],"M-estimator":[98],"and":[99,155],"Ledoit-Wolf's":[101],"shrinkage":[102,138],"while":[104],"assuming":[105],"samples":[106],"with":[107],"heavy-tailed":[108],"distribution.":[109],"Employing":[110],"recent":[111],"results":[112],"from":[113],"random":[114],"theory,":[116],"we":[117],"develop":[118],"consistent":[120],"(a":[123],"scaled":[124],"version":[125],"of)":[126],"realized":[128],"risk,":[130],"which":[131],"minimized":[133],"optimizing":[135],"online":[136],"intensity.":[139],"Our":[140],"optimization":[142],"method":[143],"shown":[145],"via":[146],"simulations":[147],"outperform":[149],"existing":[150],"methods":[151],"both":[152],"for":[153],"synthetic":[154],"real":[156],"data.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
