{"id":"https://openalex.org/W2964213435","doi":"https://doi.org/10.1109/tit.2018.2888734","title":"New Methods for Handling Singular Sample Covariance Matrices","display_name":"New Methods for Handling Singular Sample Covariance Matrices","publication_year":2018,"publication_date":"2018-12-19","ids":{"openalex":"https://openalex.org/W2964213435","doi":"https://doi.org/10.1109/tit.2018.2888734","mag":"2964213435"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2888734","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2888734","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083981154","display_name":"Gabriel H. Tucci","orcid":null},"institutions":[{"id":"https://openalex.org/I135458274","display_name":"Citigroup","ror":"https://ror.org/032xgdx47","country_code":"US","type":"other","lineage":["https://openalex.org/I135458274"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gabriel H. Tucci","raw_affiliation_strings":["Central Risk and Cash Trading in the Equities Division, Citi, New York, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Central Risk and Cash Trading in the Equities Division, Citi, New York, NY, USA","institution_ids":["https://openalex.org/I135458274"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073656495","display_name":"Ke Wang","orcid":"https://orcid.org/0000-0001-8128-3441"},"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":"Ke Wang","raw_affiliation_strings":["Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0001-8128-3441","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.21913899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"65","issue":"2","first_page":"770","last_page":"786"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9993000030517578,"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":0.9993000030517578,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9951000213623047,"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/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.7208161950111389},{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.6547966599464417},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.6421206593513489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5729572772979736},{"id":"https://openalex.org/keywords/mat\u00e9rn-covariance-function","display_name":"Mat\u00e9rn covariance function","score":0.5423574447631836},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5366145372390747},{"id":"https://openalex.org/keywords/law-of-total-covariance","display_name":"Law of total covariance","score":0.49820518493652344},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44875064492225647},{"id":"https://openalex.org/keywords/scatter-matrix","display_name":"Scatter matrix","score":0.4457554817199707},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.43622446060180664},{"id":"https://openalex.org/keywords/rational-quadratic-covariance-function","display_name":"Rational quadratic covariance function","score":0.41867995262145996},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.41316843032836914},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40583133697509766},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.3906036615371704},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3322209119796753},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32674455642700195},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.31974297761917114},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24097758531570435},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08363676071166992}],"concepts":[{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.7208161950111389},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.6547966599464417},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.6421206593513489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5729572772979736},{"id":"https://openalex.org/C118006245","wikidata":"https://www.wikidata.org/wiki/Q6792079","display_name":"Mat\u00e9rn covariance function","level":5,"score":0.5423574447631836},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5366145372390747},{"id":"https://openalex.org/C126372606","wikidata":"https://www.wikidata.org/wiki/Q6503511","display_name":"Law of total covariance","level":5,"score":0.49820518493652344},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44875064492225647},{"id":"https://openalex.org/C176917957","wikidata":"https://www.wikidata.org/wiki/Q7430596","display_name":"Scatter matrix","level":4,"score":0.4457554817199707},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.43622446060180664},{"id":"https://openalex.org/C148893098","wikidata":"https://www.wikidata.org/wiki/Q7295778","display_name":"Rational quadratic covariance function","level":5,"score":0.41867995262145996},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.41316843032836914},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40583133697509766},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.3906036615371704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3322209119796753},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32674455642700195},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.31974297761917114},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24097758531570435},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08363676071166992},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2018.2888734","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2888734","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W658559791","https://openalex.org/W1518468345","https://openalex.org/W1550150926","https://openalex.org/W1551177513","https://openalex.org/W1555149096","https://openalex.org/W1577300772","https://openalex.org/W1973243484","https://openalex.org/W1974105260","https://openalex.org/W1987235976","https://openalex.org/W1990512452","https://openalex.org/W2001879439","https://openalex.org/W2005166167","https://openalex.org/W2017911295","https://openalex.org/W2035966837","https://openalex.org/W2050626725","https://openalex.org/W2062125287","https://openalex.org/W2072207996","https://openalex.org/W2098056745","https://openalex.org/W2105502962","https://openalex.org/W2106955124","https://openalex.org/W2116414176","https://openalex.org/W2121100800","https://openalex.org/W2130351130","https://openalex.org/W2132105090","https://openalex.org/W2134984950","https://openalex.org/W2136118086","https://openalex.org/W2149755721","https://openalex.org/W2339801242","https://openalex.org/W2502759836","https://openalex.org/W2964012924","https://openalex.org/W3022776974","https://openalex.org/W3098365576","https://openalex.org/W3098757881","https://openalex.org/W3099189739","https://openalex.org/W3099609308","https://openalex.org/W3101788651","https://openalex.org/W3103699839","https://openalex.org/W3106319742","https://openalex.org/W4240060697","https://openalex.org/W4293005804","https://openalex.org/W4362230038","https://openalex.org/W6631095657","https://openalex.org/W6679963013","https://openalex.org/W6704185022"],"related_works":["https://openalex.org/W2887132723","https://openalex.org/W341081156","https://openalex.org/W3211883524","https://openalex.org/W2060816402","https://openalex.org/W4309794518","https://openalex.org/W1968000959","https://openalex.org/W2164924639","https://openalex.org/W2179028626","https://openalex.org/W8867823","https://openalex.org/W2921280830"],"abstract_inverted_index":{"The":[0,54,122],"estimation":[1],"of":[2,10,14,39,90,106],"a":[3,36,44,104],"covariance":[4,50,109],"matrix":[5,110,135],"from":[6,133],"an":[7,65],"insufficient":[8],"amount":[9],"data":[11],"is":[12,93],"one":[13],"the":[15,68,91,95,107,113,119],"most":[16],"common":[17],"problems":[18],"in":[19,62],"fields":[20],"as":[21,23],"diverse":[22],"multivariate":[24],"statistics,":[25],"wireless":[26],"communications,":[27],"signal":[28],"processing,":[29],"biology,":[30],"learning":[31],"theory,":[32],"and":[33,42,79,102,131],"finance.":[34],"In":[35,71],"joint":[37],"work":[38],"Marzetta,":[40],"Tucci":[41],"Simon,":[43],"new":[45,83],"approach":[46],"to":[47,58,85,118,125,137],"handle":[48,86],"singular":[49],"matrices":[51,115],"was":[52,57],"suggested.":[53],"main":[55],"idea":[56],"use":[59],"dimensionality":[60],"reduction":[61],"conjunction":[63],"with":[64,76,116],"average":[66],"over":[67,111],"Stiefel":[69],"manifold.":[70],"this":[72,77,87,127],"paper,":[73],"we":[74,80],"continue":[75],"research":[78],"consider":[81],"some":[82],"approaches":[84],"problem.":[88],"One":[89],"methods":[92],"called":[94],"mean":[96],"conjugate":[97],"estimator":[98],"under":[99],"Ewens":[100,120],"measure":[101],"uses":[103],"randomization":[105],"sample":[108],"all":[112],"permutation":[114],"respect":[117],"measure.":[121],"techniques":[123],"used":[124],"attack":[126],"problem":[128],"are":[129],"broad":[130],"run":[132],"random":[134],"theory":[136],"combinatorics.":[138]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}