{"id":"https://openalex.org/W3103809946","doi":"https://doi.org/10.1109/tit.2012.2232705","title":"Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors","display_name":"Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors","publication_year":2012,"publication_date":"2012-12-08","ids":{"openalex":"https://openalex.org/W3103809946","doi":"https://doi.org/10.1109/tit.2012.2232705","mag":"3103809946"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2232705","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/1204.5635","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058914830","display_name":"David Ram\u00edrez","orcid":"https://orcid.org/0000-0002-6883-7742"},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"funder","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"David Ramirez","raw_affiliation_strings":["Signal and System Theory Group, Universit\u00e4t Paderborn, Paderborn, Germany"],"affiliations":[{"raw_affiliation_string":"Signal and System Theory Group, Universit\u00e4t Paderborn, Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071269640","display_name":"Javier V\u00eda","orcid":"https://orcid.org/0000-0001-7853-0069"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"funder","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Javier Via","raw_affiliation_strings":["Department of Communications Engineering, University of Cantabria, Santander, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Communications Engineering, University of Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059078809","display_name":"Ignacio Santamar\u0131\u0301a","orcid":"https://orcid.org/0000-0003-0040-7436"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"funder","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ignacio Santamaria","raw_affiliation_strings":["Department of Communications Engineering, University of Cantabria, Santander, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Communications Engineering, University of Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080469112","display_name":"Louis L. Scharf","orcid":"https://orcid.org/0000-0003-1764-9335"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"funder","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Louis L. Scharf","raw_affiliation_strings":["Department of Mathematics and the Department of Statistics, Colorado State University, Fort Collins, CO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and the Department of Statistics, Colorado State University, Fort Collins, CO, USA","institution_ids":["https://openalex.org/I92446798"]}]}],"institution_assertions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.412,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":50,"citation_normalized_percentile":{"value":0.89914,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"59","issue":"4","first_page":"2128","last_page":"2141"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998,"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":0.9998,"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9983,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9954,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sphericity","display_name":"Sphericity","score":0.511622}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.80070996},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.6371007},{"id":"https://openalex.org/C9483764","wikidata":"https://www.wikidata.org/wiki/Q585740","display_name":"Likelihood-ratio test","level":2,"score":0.6087817},{"id":"https://openalex.org/C120639","wikidata":"https://www.wikidata.org/wiki/Q7068958","display_name":"Null distribution","level":4,"score":0.590814},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.58526134},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5845273},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.5843571},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5620467},{"id":"https://openalex.org/C173913448","wikidata":"https://www.wikidata.org/wiki/Q1375687","display_name":"Sphericity","level":2,"score":0.511622},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.5098395},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.4990089},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46513432},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.44048288},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39501113},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.38907743},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25468782},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2232705","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.5635","pdf_url":"http://arxiv.org/pdf/1204.5635","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":null,"pdf_url":"https://arxiv.org/pdf/1204.5635.pdf","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1204.5635","pdf_url":"https://arxiv.org/pdf/1204.5635","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.1204.5635","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.5635","pdf_url":"http://arxiv.org/pdf/1204.5635","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":["https://openalex.org/W2029399534","https://openalex.org/W3103809946"],"referenced_works_count":45,"referenced_works":["https://openalex.org/W13022817","https://openalex.org/W1536100164","https://openalex.org/W1540313536","https://openalex.org/W1578953027","https://openalex.org/W1595105216","https://openalex.org/W1600738178","https://openalex.org/W1899585731","https://openalex.org/W1964626789","https://openalex.org/W1965392255","https://openalex.org/W1980455221","https://openalex.org/W2003710388","https://openalex.org/W2014101702","https://openalex.org/W2028002800","https://openalex.org/W2035072290","https://openalex.org/W2036248065","https://openalex.org/W2037295216","https://openalex.org/W2041740644","https://openalex.org/W2073839155","https://openalex.org/W2084928760","https://openalex.org/W2090796575","https://openalex.org/W2101478599","https://openalex.org/W2118880464","https://openalex.org/W2138255796","https://openalex.org/W2144940556","https://openalex.org/W2147153302","https://openalex.org/W2150365048","https://openalex.org/W2152121970","https://openalex.org/W2154449558","https://openalex.org/W2155421090","https://openalex.org/W2155875116","https://openalex.org/W2159582847","https://openalex.org/W2159965718","https://openalex.org/W2163852636","https://openalex.org/W2165800172","https://openalex.org/W2285653497","https://openalex.org/W2314024971","https://openalex.org/W2468941065","https://openalex.org/W3104928457","https://openalex.org/W3118891004","https://openalex.org/W3205598854","https://openalex.org/W4210572675","https://openalex.org/W4233959632","https://openalex.org/W4238149895","https://openalex.org/W4289255398","https://openalex.org/W65255600"],"related_works":["https://openalex.org/W82908857","https://openalex.org/W4298294561","https://openalex.org/W4297848787","https://openalex.org/W3153979494","https://openalex.org/W2951620698","https://openalex.org/W2950259315","https://openalex.org/W2083331322","https://openalex.org/W2019837664","https://openalex.org/W1967100726","https://openalex.org/W1010129004"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,162,189],"study":[4,163],"the":[5,15,19,32,36,44,47,58,69,76,81,106,109,120,126,148,153,157,164,168,171,181,192,197,205,214,217],"existence":[6],"of":[7,17,22,25,38,46,68,108,128,133,156,200,204,216],"locally":[8],"most":[9],"powerful":[10],"invariant":[11,78,111],"tests":[12],"(LMPIT)":[13],"for":[14,35,80,119,184,187],"problem":[16,83,127],"testing":[18,129],"covariance":[20,207],"structure":[21],"a":[23,96,131,201],"set":[24,132],"Gaussian":[26,138,185],"random":[27,139],"vectors.":[28],"The":[29,66],"LMPIT":[30,70,149,193],"is":[31,95,150,194],"optimal":[33],"test":[34,64,183],"case":[37,165],"close":[39],"hypotheses,":[40,91],"among":[41],"those":[42],"satisfying":[43],"invariances":[45],"problem,":[48],"and":[49,84,145,176],"in":[50,93,166],"practical":[51],"scenarios":[52],"can":[53],"provide":[54,221],"better":[55,222],"performance":[56,215],"than":[57,224],"typically":[59],"used":[60],"generalized":[61],"likelihood":[62],"ratio":[63,107],"(GLRT).":[65],"derivation":[67],"usually":[71],"requires":[72],"one":[73],"to":[74],"find":[75],"maximal":[77,110,121],"statistic":[79],"detection":[82],"then":[85],"derive":[86],"its":[87],"distribution":[88],"under":[89,170],"both":[90],"which":[92,167,188,220],"general":[94],"rather":[97],"involved":[98],"procedure.":[99],"As":[100],"an":[101,116],"alternative,":[102],"Wijsman's":[103],"theorem":[104],"provides":[105],"densities":[112],"without":[113],"even":[114],"finding":[115],"explicit":[117],"expression":[118],"invariant.":[122],"We":[123],"first":[124],"consider":[125],"whether":[130],"N":[136],"-dimensional":[137],"vectors":[140,169],"are":[141,174],"uncorrelated":[142,175],"or":[143],"not,":[144],"show":[146,190],"that":[147,179,191],"given":[151,195],"by":[152,196],"Frobenius":[154,198],"norm":[155,199],"sample":[158,206],"coherence":[159],"matrix.":[160,208],"Second,":[161],"null":[172],"hypothesis":[173],"identically":[177],"distributed,":[178],"is,":[180],"sphericity":[182],"vectors,":[186],"normalized":[202],"version":[203],"Finally,":[209],"some":[210],"numerical":[211],"examples":[212],"illustrate":[213],"proposed":[218],"tests,":[219],"results":[223],"their":[225],"GLRT":[226],"counterparts.":[227]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3103809946","counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":1}],"updated_date":"2025-04-23T20:06:19.599969","created_date":"2020-11-23"}