{"id":"https://openalex.org/W7154955523","doi":"https://doi.org/10.1109/tit.2026.3685246","title":"Simultaneous Inference for Covariance and Precision Matrices of Long-Range Dependent Time Series","display_name":"Simultaneous Inference for Covariance and Precision Matrices of Long-Range Dependent Time Series","publication_year":2026,"publication_date":"2026-04-20","ids":{"openalex":"https://openalex.org/W7154955523","doi":"https://doi.org/10.1109/tit.2026.3685246"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2026.3685246","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3685246","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/A5108906088","display_name":"Percy S. Zhai","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Percy S. Zhai","raw_affiliation_strings":["Booth School of Business, The University of Chicago, Chicago, IL, USA"],"raw_orcid":"https://orcid.org/0009-0009-6295-5279","affiliations":[{"raw_affiliation_string":"Booth School of Business, The University of Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016868056","display_name":"Mladen Kolar","orcid":"https://orcid.org/0000-0001-7353-3404"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mladen Kolar","raw_affiliation_strings":["Marshall School of Business, University of Southern California, Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Marshall School of Business, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036683934","display_name":"Wei Biao Wu","orcid":"https://orcid.org/0000-0003-4310-9965"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Biao Wu","raw_affiliation_strings":["Department of Statistics, The University of Chicago, Chicago, IL, USA"],"raw_orcid":"https://orcid.org/0000-0003-4310-9965","affiliations":[{"raw_affiliation_string":"Department of Statistics, The University of Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"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":0,"citation_normalized_percentile":{"value":0.48140889,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"6","first_page":"4246","last_page":"4296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.43369999527931213,"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"}},"topics":[{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.43369999527931213,"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"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.08139999955892563,"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/T12205","display_name":"Time Series Analysis and Forecasting","score":0.06480000168085098,"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/series","display_name":"Series (stratigraphy)","score":0.5831000208854675},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5644000172615051},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5584999918937683},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.43130001425743103},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.39329999685287476},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.3781999945640564},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.3659999966621399},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.3400000035762787}],"concepts":[{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5831000208854675},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5644000172615051},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5584999918937683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.536899983882904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4796999990940094},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46219998598098755},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.43130001425743103},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4000000059604645},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.39329999685287476},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.3659999966621399},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3400000035762787},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.3124000132083893},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.2815999984741211},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.28130000829696655},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.2700999975204468},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.2574000060558319},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2026.3685246","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3685246","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":[{"id":"https://openalex.org/G3484525887","display_name":null,"funder_award_id":"NSF/DMS-2027723","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8241236867","display_name":null,"funder_award_id":"NSF/DMS-2311249","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W55912154","https://openalex.org/W817447733","https://openalex.org/W1578928397","https://openalex.org/W1821241690","https://openalex.org/W1895906169","https://openalex.org/W1963657942","https://openalex.org/W1970417896","https://openalex.org/W1974443622","https://openalex.org/W1974554864","https://openalex.org/W1975925591","https://openalex.org/W1976623182","https://openalex.org/W1983139221","https://openalex.org/W1985488135","https://openalex.org/W1988645907","https://openalex.org/W1989727964","https://openalex.org/W2005424182","https://openalex.org/W2010651179","https://openalex.org/W2010824638","https://openalex.org/W2015895869","https://openalex.org/W2017335040","https://openalex.org/W2027470276","https://openalex.org/W2028395910","https://openalex.org/W2028722600","https://openalex.org/W2032291279","https://openalex.org/W2054478558","https://openalex.org/W2057285652","https://openalex.org/W2058046532","https://openalex.org/W2058765104","https://openalex.org/W2063167566","https://openalex.org/W2067184061","https://openalex.org/W2070794090","https://openalex.org/W2072864444","https://openalex.org/W2074957274","https://openalex.org/W2077514460","https://openalex.org/W2078411132","https://openalex.org/W2118443367","https://openalex.org/W2130126601","https://openalex.org/W2131543796","https://openalex.org/W2137387582","https://openalex.org/W2137696270","https://openalex.org/W2141805926","https://openalex.org/W2146437136","https://openalex.org/W2149919638","https://openalex.org/W2167868121","https://openalex.org/W2170797424","https://openalex.org/W2277328580","https://openalex.org/W2503608075","https://openalex.org/W2524946712","https://openalex.org/W2596998183","https://openalex.org/W2766710231","https://openalex.org/W2805186087","https://openalex.org/W2908289211","https://openalex.org/W2921129218","https://openalex.org/W2951049961","https://openalex.org/W2952504266","https://openalex.org/W2952875417","https://openalex.org/W2963345331","https://openalex.org/W2963629083","https://openalex.org/W2964914639","https://openalex.org/W2965497096","https://openalex.org/W2981639905","https://openalex.org/W2982682025","https://openalex.org/W2996387942","https://openalex.org/W3111733686","https://openalex.org/W3124120322","https://openalex.org/W3200683718","https://openalex.org/W4230642157","https://openalex.org/W4367850813","https://openalex.org/W4390055434","https://openalex.org/W4392477123"],"related_works":[],"abstract_inverted_index":{"For":[0],"time":[1,89],"series":[2,90],"with":[3,67,94],"long-range":[4],"temporal":[5,76],"dependence,":[6],"inference":[7],"for":[8,28,102],"covariance":[9,42,81,116],"and":[10,44,55,117],"precision":[11,103,118],"matrices":[12],"is":[13,110],"non-trivial.":[14],"We":[15,61],"propose":[16],"a":[17,25,64],"Berry-Esseen":[18],"type":[19],"Gaussian":[20,47],"approximation":[21,54],"result":[22,66],"that":[23],"gives":[24],"finite-sample":[26],"bound":[27],"the":[29,33,37,45,86,113],"Kolmogorov":[30],"distance":[31],"between":[32],"infinity":[34],"norms":[35],"of":[36,40,88,115],"estimation":[38],"error":[39],"sample":[41,95],"matrix":[43,104],"corresponding":[46],"approximation.":[48],"The":[49],"method":[50],"utilizes":[51],"martingale":[52],"andm-dependent":[53],"relies":[56],"on":[57,80,112],"constructing":[58],"triadic":[59],"blocks.":[60],"also":[62],"establish":[63],"bootstrapping":[65],"block":[68],"sampling":[69],"method,":[70],"which":[71],"preserves":[72],"validity":[73],"despite":[74],"strong":[75],"dependence.":[77],"Our":[78],"results":[79,98],"allow":[82],"ultra-high-dimensional":[83],"settings":[84],"where":[85],"dimension":[87],"can":[91,99],"grow":[92],"sub-exponentially":[93],"size.":[96],"Similar":[97],"be":[100],"built":[101],"under":[105],"low-dimensional":[106],"settings.":[107],"No":[108],"assumption":[109],"required":[111],"structure":[114],"matrices.":[119]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2026-04-21T00:00:00"}
