{"id":"https://openalex.org/W2930543415","doi":"https://doi.org/10.1080/03610918.2019.1588315","title":"On variance of sample matrix eigenvalue","display_name":"On variance of sample matrix eigenvalue","publication_year":2019,"publication_date":"2019-04-03","ids":{"openalex":"https://openalex.org/W2930543415","doi":"https://doi.org/10.1080/03610918.2019.1588315","mag":"2930543415"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2019.1588315","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1588315","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/A5065617474","display_name":"Janusz Wywia\u0142","orcid":"https://orcid.org/0000-0002-3392-1688"},"institutions":[{"id":"https://openalex.org/I188922065","display_name":"University of Economics in Katowice","ror":"https://ror.org/01vxt3d40","country_code":"PL","type":"education","lineage":["https://openalex.org/I188922065"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Janusz L. Wywia\u0142","raw_affiliation_strings":["Department of Statistics, Econometrics and Mathematisc, Katowice University of Economics, Katowice, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Econometrics and Mathematisc, Katowice University of Economics, Katowice, Poland","institution_ids":["https://openalex.org/I188922065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053538046","display_name":"Grzegorz Sitek","orcid":"https://orcid.org/0000-0002-7191-8631"},"institutions":[{"id":"https://openalex.org/I188922065","display_name":"University of Economics in Katowice","ror":"https://ror.org/01vxt3d40","country_code":"PL","type":"education","lineage":["https://openalex.org/I188922065"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Grzegorz Sitek","raw_affiliation_strings":["Department of Statistics, Econometrics and Mathematisc, Katowice University of Economics, Katowice, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Econometrics and Mathematisc, Katowice University of Economics, Katowice, Poland","institution_ids":["https://openalex.org/I188922065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065617474"],"corresponding_institution_ids":["https://openalex.org/I188922065"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04559124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"50","issue":"7","first_page":"1943","last_page":"1954"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9897000193595886,"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":0.9897000193595886,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9882000088691711,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9735000133514404,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.7488553524017334},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6894550919532776},{"id":"https://openalex.org/keywords/bias-of-an-estimator","display_name":"Bias of an estimator","score":0.5738465785980225},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5458812713623047},{"id":"https://openalex.org/keywords/variance-function","display_name":"Variance function","score":0.5405427813529968},{"id":"https://openalex.org/keywords/variance-based-sensitivity-analysis","display_name":"Variance-based sensitivity analysis","score":0.5173194408416748},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4981954097747803},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4884618818759918},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.45850852131843567},{"id":"https://openalex.org/keywords/sample-variance","display_name":"Sample variance","score":0.4558119475841522},{"id":"https://openalex.org/keywords/statistic","display_name":"Statistic","score":0.44808071851730347},{"id":"https://openalex.org/keywords/consistent-estimator","display_name":"Consistent estimator","score":0.4295235574245453},{"id":"https://openalex.org/keywords/law-of-total-variance","display_name":"Law of total variance","score":0.4261653423309326},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.3959107995033264},{"id":"https://openalex.org/keywords/one-way-analysis-of-variance","display_name":"One-way analysis of variance","score":0.3449152112007141},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.18234840035438538},{"id":"https://openalex.org/keywords/analysis-of-variance","display_name":"Analysis of variance","score":0.13787412643432617},{"id":"https://openalex.org/keywords/conditional-variance","display_name":"Conditional variance","score":0.09908542037010193}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7488553524017334},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6894550919532776},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.5738465785980225},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5458812713623047},{"id":"https://openalex.org/C120488996","wikidata":"https://www.wikidata.org/wiki/Q17016064","display_name":"Variance function","level":3,"score":0.5405427813529968},{"id":"https://openalex.org/C108311543","wikidata":"https://www.wikidata.org/wiki/Q7915756","display_name":"Variance-based sensitivity analysis","level":4,"score":0.5173194408416748},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4981954097747803},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4884618818759918},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.45850852131843567},{"id":"https://openalex.org/C2993021520","wikidata":"https://www.wikidata.org/wiki/Q175199","display_name":"Sample variance","level":3,"score":0.4558119475841522},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.44808071851730347},{"id":"https://openalex.org/C164172150","wikidata":"https://www.wikidata.org/wiki/Q1782585","display_name":"Consistent estimator","level":4,"score":0.4295235574245453},{"id":"https://openalex.org/C18934984","wikidata":"https://www.wikidata.org/wiki/Q1055879","display_name":"Law of total variance","level":5,"score":0.4261653423309326},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.3959107995033264},{"id":"https://openalex.org/C152587130","wikidata":"https://www.wikidata.org/wiki/Q7092351","display_name":"One-way analysis of variance","level":3,"score":0.3449152112007141},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.18234840035438538},{"id":"https://openalex.org/C99476002","wikidata":"https://www.wikidata.org/wiki/Q42297","display_name":"Analysis of variance","level":2,"score":0.13787412643432617},{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.09908542037010193},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"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/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","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},{"id":"https://openalex.org/C23922673","wikidata":"https://www.wikidata.org/wiki/Q180752","display_name":"Autoregressive conditional heteroskedasticity","level":3,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610918.2019.1588315","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1588315","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1973051875","https://openalex.org/W1973335304","https://openalex.org/W1977424707","https://openalex.org/W1981492379","https://openalex.org/W1996957620","https://openalex.org/W2011755304","https://openalex.org/W2028810406","https://openalex.org/W2036632722","https://openalex.org/W2063698478","https://openalex.org/W2088309921","https://openalex.org/W2110011782","https://openalex.org/W2115784903","https://openalex.org/W2334996892","https://openalex.org/W2487122920","https://openalex.org/W2777019853","https://openalex.org/W2999392993","https://openalex.org/W4213099427","https://openalex.org/W4255783720","https://openalex.org/W4255896674","https://openalex.org/W4300029251"],"related_works":["https://openalex.org/W2587668322","https://openalex.org/W78698718","https://openalex.org/W341703941","https://openalex.org/W2041983147","https://openalex.org/W1968762217","https://openalex.org/W2006580754","https://openalex.org/W2125072374","https://openalex.org/W1868007872","https://openalex.org/W2102710528","https://openalex.org/W2337986376"],"abstract_inverted_index":{"The":[0,32,78],"variance":[1,33,58,74,82,89],"of":[2,14,21,34,48,59,70,73,81,90,97,102],"a":[3,12,22,46,91],"matrix":[4],"eigenvalue":[5,36],"estimator":[6,10,37,63],"is":[7,11,28,38,64,76,94],"considered.":[8],"This":[9],"function":[13,47],"simple":[15,49],"random":[16,24,50],"sample":[17,51,103],"variances":[18],"and":[19],"covariances":[20],"multidimensional":[23],"variable":[25],"whose":[26],"distribution":[27],"not":[29],"necessarily":[30],"normal.":[31],"the":[35,42,57,60,71,88,95],"approximated":[39],"based":[40],"on":[41],"Taylor":[43],"expansion":[44],"for":[45,55],"moments.":[52,104],"A":[53,67],"method":[54],"approximating":[56],"canonical":[61],"correlation":[62],"also":[65],"proposed.":[66],"simulation":[68],"analysis":[69],"accuracy":[72],"estimation":[75],"presented.":[77],"considered":[79],"approximation":[80],"can":[83],"be":[84],"applied":[85],"to":[86],"assessing":[87],"statistic":[92],"which":[93],"solution":[96],"any":[98],"implicit":[99],"interdependence":[100],"functions":[101]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
