{"id":"https://openalex.org/W3102813955","doi":"https://doi.org/10.1109/tit.2016.2530090","title":"SURE Information Criteria for Large Covariance Matrix Estimation and Their Asymptotic Properties","display_name":"SURE Information Criteria for Large Covariance Matrix Estimation and Their Asymptotic Properties","publication_year":2016,"publication_date":"2016-02-15","ids":{"openalex":"https://openalex.org/W3102813955","doi":"https://doi.org/10.1109/tit.2016.2530090","mag":"3102813955"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2530090","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2530090","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1406.6514","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Danning Li","orcid":null},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]},{"id":"https://openalex.org/I4210136497","display_name":"Jilin Medical University","ror":"https://ror.org/03mzw7781","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136497"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Danning Li","raw_affiliation_strings":["School of Mathematics, Jilin University, Jilin, China","Statistical Laboratory, University of Cambridge, Cambridge, U.K"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Jilin University, Jilin, China","institution_ids":["https://openalex.org/I4210136497","https://openalex.org/I194450716"]},{"raw_affiliation_string":"Statistical Laboratory, University of Cambridge, Cambridge, U.K","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Hui Zou","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hui Zou","raw_affiliation_strings":["University of Minnesota, Minneapolis, MN, USA"],"affiliations":[{"raw_affiliation_string":"University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I194450716","https://openalex.org/I4210136497"],"apc_list":null,"apc_paid":null,"fwci":1.8466,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.87776915,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"62","issue":"4","first_page":"2153","last_page":"2169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.8108000159263611,"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":0.8108000159263611,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.05620000138878822,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10891","display_name":"Radar Systems and Signal Processing","score":0.021299999207258224,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.7976999878883362},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.7239000201225281},{"id":"https://openalex.org/keywords/rational-quadratic-covariance-function","display_name":"Rational quadratic covariance function","score":0.6103000044822693},{"id":"https://openalex.org/keywords/akaike-information-criterion","display_name":"Akaike information criterion","score":0.5924000144004822},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5891000032424927},{"id":"https://openalex.org/keywords/law-of-total-covariance","display_name":"Law of total covariance","score":0.5837000012397766},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.5738999843597412},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.565500020980835},{"id":"https://openalex.org/keywords/mat\u00e9rn-covariance-function","display_name":"Mat\u00e9rn covariance function","score":0.5034999847412109}],"concepts":[{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.7976999878883362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7870000004768372},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.7239000201225281},{"id":"https://openalex.org/C148893098","wikidata":"https://www.wikidata.org/wiki/Q7295778","display_name":"Rational quadratic covariance function","level":5,"score":0.6103000044822693},{"id":"https://openalex.org/C126674687","wikidata":"https://www.wikidata.org/wiki/Q1662573","display_name":"Akaike information criterion","level":2,"score":0.5924000144004822},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5891000032424927},{"id":"https://openalex.org/C126372606","wikidata":"https://www.wikidata.org/wiki/Q6503511","display_name":"Law of total covariance","level":5,"score":0.5837000012397766},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.5738999843597412},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.565500020980835},{"id":"https://openalex.org/C118006245","wikidata":"https://www.wikidata.org/wiki/Q6792079","display_name":"Mat\u00e9rn covariance function","level":5,"score":0.5034999847412109},{"id":"https://openalex.org/C176917957","wikidata":"https://www.wikidata.org/wiki/Q7430596","display_name":"Scatter matrix","level":4,"score":0.4747999906539917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4307999908924103},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.40130001306533813},{"id":"https://openalex.org/C205555498","wikidata":"https://www.wikidata.org/wiki/Q505588","display_name":"CMA-ES","level":4,"score":0.3880999982357025},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.382999986410141},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.36800000071525574},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C168136583","wikidata":"https://www.wikidata.org/wiki/Q1988242","display_name":"Bayesian information criterion","level":2,"score":0.3598000109195709},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.34369999170303345},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.3409999907016754},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3352000117301941},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.29120001196861267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2865999937057495},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C164172150","wikidata":"https://www.wikidata.org/wiki/Q1782585","display_name":"Consistent estimator","level":4,"score":0.2669999897480011},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.26330000162124634},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.2628999948501587},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2016.2530090","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2530090","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"},{"id":"pmh:oai:arXiv.org:1406.6514","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1406.6514","pdf_url":"https://arxiv.org/pdf/1406.6514","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1406.6514","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1406.6514","pdf_url":"https://arxiv.org/pdf/1406.6514","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":28,"referenced_works":["https://openalex.org/W1487955057","https://openalex.org/W1502338185","https://openalex.org/W1520752838","https://openalex.org/W1971031270","https://openalex.org/W1972500015","https://openalex.org/W1981638497","https://openalex.org/W1995691260","https://openalex.org/W2008681993","https://openalex.org/W2013805643","https://openalex.org/W2017911295","https://openalex.org/W2054640142","https://openalex.org/W2057535756","https://openalex.org/W2063978378","https://openalex.org/W2063986268","https://openalex.org/W2072207996","https://openalex.org/W2078038009","https://openalex.org/W2084913894","https://openalex.org/W2089887770","https://openalex.org/W2098056745","https://openalex.org/W2114180688","https://openalex.org/W2128033135","https://openalex.org/W2130351130","https://openalex.org/W2591778798","https://openalex.org/W4249991467","https://openalex.org/W4255521522","https://openalex.org/W4293005804","https://openalex.org/W6629078793","https://openalex.org/W6674960185"],"related_works":[],"abstract_inverted_index":{"Consider":[0],"n":[1,25,81],"independent":[2],"and":[3,54,97,169,219,230],"identically":[4],"distributed":[5],"p-dimensional":[6],"Gaussian":[7],"random":[8],"vectors":[9],"with":[10,208],"covariance":[11,44,76,117,140,154,176,188,236],"matrix":[12,45,118,141,155,177,189,237],"\u03a3.":[13],"The":[14],"problem":[15],"of":[16,30,74,109,134,138,163],"estimating":[17],"\u03a3":[18],"when":[19,78],"p":[20,79],"is":[21,37,122,127,190],"much":[22],"larger":[23],"than":[24],"has":[26],"received":[27],"a":[28,52,107],"lot":[29],"attention":[31],"in":[32,66,102],"recent":[33],"years.":[34],"Yet,":[35],"little":[36],"known":[38],"about":[39],"the":[40,57,72,88,135,139,159,166,170,175,181,186,205,228],"information":[41,99,232],"criterion":[42,53,100,233],"for":[43,116,234],"estimation.":[46],"How":[47],"to":[48,62,211],"properly":[49],"define":[50],"such":[51],"what":[55],"are":[56],"statistical":[58],"properties?":[59],"We":[60],"attempt":[61],"answer":[63],"these":[64],"questions":[65],"this":[67],"paper":[68],"by":[69,87,114,147,180,196],"focusing":[70],"on":[71],"estimation":[73,95],"bandable":[75],"matrices":[77],">":[80],"but":[82],"log(p)":[83],"=":[84],"o(n).":[85],"Motivated":[86],"deep":[89],"connection":[90],"between":[91],"Stein's":[92],"unbiased":[93,132],"risk":[94,137],"(SURE)":[96],"Akaike":[98],"(AIC)":[101],"regression":[103],"models,":[104],"we":[105,144,157,193,203],"propose":[106],"family":[108],"generalized":[110],"SURE":[111,198,220],"(SUREc)":[112],"indexed":[113],"c":[115,121,126],"estimation,":[119,238],"where":[120],"some":[123],"constant.":[124],"When":[125,185],"2,":[128],"SURE2":[129,149,218],"provides":[130],"an":[131],"estimator":[133,172,178],"Frobenius":[136,167],"estimator.":[142],"Furthermore,":[143],"show":[145],"that":[146,195,217],"minimizing":[148,197],"over":[150],"all":[151],"possible":[152],"banding":[153],"estimators,":[156],"attain":[158],"minimax":[160],"optimal":[161],"rate":[162],"convergence":[164],"under":[165],"norm,":[168],"resulting":[171],"behaves":[173],"like":[174],"obtained":[179],"so-called":[182],"oracle":[183],"tuning.":[184],"true":[187,206],"exactly":[191],"banded,":[192],"prove":[194],"<sub":[199,221],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[200,222],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">log(n)</sub>":[201,223],",":[202],"select":[204],"bandwidth":[207],"probability":[209],"tending":[210],"one.":[212],"Therefore,":[213],"our":[214],"analysis":[215],"indicates":[216],"can":[224],"be":[225],"regarded":[226],"as":[227],"AIC":[229],"Bayesian":[231],"large":[235],"respectively.":[239]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-11-23T00:00:00"}
