{"id":"https://openalex.org/W3194235159","doi":"https://doi.org/10.1080/03610918.2021.1960998","title":"Distribution approximation of covariance matrix eigenvalues","display_name":"Distribution approximation of covariance matrix eigenvalues","publication_year":2021,"publication_date":"2021-08-24","ids":{"openalex":"https://openalex.org/W3194235159","doi":"https://doi.org/10.1080/03610918.2021.1960998","mag":"3194235159"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2021.1960998","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2021.1960998","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","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/A5103288561","display_name":"Shin-ichi Tsukada","orcid":null},"institutions":[{"id":"https://openalex.org/I63030401","display_name":"Meisei University","ror":"https://ror.org/022yhjq53","country_code":"JP","type":"education","lineage":["https://openalex.org/I63030401"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shin-ichi Tsukada","raw_affiliation_strings":["School of Education, Meisei University","School of Education, Meisei University, Hino City, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"School of Education, Meisei University","institution_ids":["https://openalex.org/I63030401"]},{"raw_affiliation_string":"School of Education, Meisei University, Hino City, Tokyo, Japan","institution_ids":["https://openalex.org/I63030401"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110480680","display_name":"Takatoshi Sugiyama","orcid":null},"institutions":[{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takatoshi Sugiyama","raw_affiliation_strings":["Institute of Statistical Science","Institute of Statistical Science, Suginami-ku, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Institute of Statistical Science","institution_ids":[]},{"raw_affiliation_string":"Institute of Statistical Science, Suginami-ku, Tokyo, Japan","institution_ids":["https://openalex.org/I4210134673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103288561"],"corresponding_institution_ids":["https://openalex.org/I63030401"],"apc_list":null,"apc_paid":null,"fwci":0.232,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58457032,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"52","issue":"9","first_page":"4313","last_page":"4325"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9990000128746033,"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":0.9990000128746033,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9950000047683716,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.733691930770874},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6568691730499268},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.6329362392425537},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.5821885466575623},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.578896701335907},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5324457883834839},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4834192991256714},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4580293297767639},{"id":"https://openalex.org/keywords/multivariate-normal-distribution","display_name":"Multivariate normal distribution","score":0.4217125177383423},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3327348232269287},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10454392433166504}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.733691930770874},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6568691730499268},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.6329362392425537},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5821885466575623},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.578896701335907},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5324457883834839},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4834192991256714},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4580293297767639},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.4217125177383423},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3327348232269287},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10454392433166504},{"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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"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:10.1080/03610918.2021.1960998","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2021.1960998","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1015709728","https://openalex.org/W1968210270","https://openalex.org/W1971078296","https://openalex.org/W1986844693","https://openalex.org/W1995371845","https://openalex.org/W2008630157","https://openalex.org/W2015833157","https://openalex.org/W2015932327","https://openalex.org/W2027616605","https://openalex.org/W2045848426","https://openalex.org/W2076123018","https://openalex.org/W2083493127","https://openalex.org/W2097267203","https://openalex.org/W2107704778","https://openalex.org/W2110011782","https://openalex.org/W2165918462","https://openalex.org/W4229520475","https://openalex.org/W4301689241"],"related_works":["https://openalex.org/W2013048391","https://openalex.org/W2886934452","https://openalex.org/W1489099099","https://openalex.org/W2220190985","https://openalex.org/W2346846619","https://openalex.org/W2024369332","https://openalex.org/W2417295580","https://openalex.org/W1974955043","https://openalex.org/W4250921637","https://openalex.org/W1840639769"],"abstract_inverted_index":{"In":[0],"multivariate":[1],"analysis,":[2],"the":[3,6,40],"eigenvalues":[4],"of":[5],"covariance":[7],"matrix":[8],"are":[9,27],"crucial.":[10],"Thus,":[11],"there":[12,26],"is":[13],"a":[14,20,44],"demand":[15],"among":[16],"users":[17],"to":[18],"find":[19],"good,":[21],"easy-to-use":[22],"chi-squared":[23,41],"approximation.":[24],"However,":[25],"few":[28],"good":[29],"approximations":[30],"for":[31],"eigenvalues.":[32],"Therefore,":[33],"in":[34],"this":[35],"paper,":[36],"we":[37],"focus":[38],"on":[39],"approximation,":[42],"proposing":[43],"new":[45],"approximation":[46],"and":[47],"investigating":[48],"its":[49],"accuracy.":[50]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-02-09T05:59:30.833894","created_date":"2025-10-10T00:00:00"}