{"id":"https://openalex.org/W2029399534","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/W2029399534","doi":"https://doi.org/10.1109/tit.2012.2232705","mag":"2029399534"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2232705","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_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/1204.5635","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"David Ramirez","orcid":null},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","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"],"raw_orcid":null,"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":null,"display_name":"Javier Via","orcid":null},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Communications Engineering, University of Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ignacio Santamaria","orcid":null},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Communications Engineering, University of Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":null,"display_name":"Louis L. Scharf","orcid":null},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","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"],"raw_orcid":null,"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"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9744,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.93870157,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"4","first_page":"2128","last_page":"2141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.89410001039505,"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":0.89410001039505,"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":0.03709999844431877,"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":0.021700000390410423,"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/covariance","display_name":"Covariance","score":0.6468999981880188},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6044999957084656},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5953999757766724},{"id":"https://openalex.org/keywords/sphericity","display_name":"Sphericity","score":0.5565999746322632},{"id":"https://openalex.org/keywords/likelihood-ratio-test","display_name":"Likelihood-ratio test","score":0.5489000082015991},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.5390999913215637},{"id":"https://openalex.org/keywords/null-distribution","display_name":"Null distribution","score":0.4932999908924103},{"id":"https://openalex.org/keywords/test-statistic","display_name":"Test statistic","score":0.4878999888896942},{"id":"https://openalex.org/keywords/multivariate-random-variable","display_name":"Multivariate random variable","score":0.4869000017642975}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8422999978065491},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6468999981880188},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6044999957084656},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5953999757766724},{"id":"https://openalex.org/C173913448","wikidata":"https://www.wikidata.org/wiki/Q1375687","display_name":"Sphericity","level":2,"score":0.5565999746322632},{"id":"https://openalex.org/C9483764","wikidata":"https://www.wikidata.org/wiki/Q585740","display_name":"Likelihood-ratio test","level":2,"score":0.5489000082015991},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.5390999913215637},{"id":"https://openalex.org/C120639","wikidata":"https://www.wikidata.org/wiki/Q7068958","display_name":"Null distribution","level":4,"score":0.4932999908924103},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.4878999888896942},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.4869000017642975},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.46369999647140503},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.444599986076355},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.42809998989105225},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.399399995803833},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.3937000036239624},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3880000114440918},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.3481000065803528},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3434000015258789},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3280999958515167},{"id":"https://openalex.org/C100279318","wikidata":"https://www.wikidata.org/wiki/Q467440","display_name":"Sample space","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.3057999908924103},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.30059999227523804},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.29280000925064087},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C169345407","wikidata":"https://www.wikidata.org/wiki/Q8216221","display_name":"Uncorrelated","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2012.2232705","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_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:1204.5635","is_oa":true,"landing_page_url":"http://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_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:1204.5635","is_oa":true,"landing_page_url":"http://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_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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W65255600","https://openalex.org/W1540313536","https://openalex.org/W1600738178","https://openalex.org/W1899585731","https://openalex.org/W1980455221","https://openalex.org/W2003710388","https://openalex.org/W2028002800","https://openalex.org/W2035072290","https://openalex.org/W2037295216","https://openalex.org/W2041740644","https://openalex.org/W2084928760","https://openalex.org/W2090796575","https://openalex.org/W2101478599","https://openalex.org/W2118880464","https://openalex.org/W2122496388","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/W2314024971","https://openalex.org/W3118891004","https://openalex.org/W4210572675","https://openalex.org/W4233959632","https://openalex.org/W6631820835"],"related_works":[],"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],"<i":[134],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[135],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</i>":[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]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2016-06-24T00:00:00"}