{"id":"https://openalex.org/W2103641619","doi":"https://doi.org/10.1109/tit.2011.2104670","title":"Universal and Composite Hypothesis Testing via Mismatched Divergence","display_name":"Universal and Composite Hypothesis Testing via Mismatched Divergence","publication_year":2011,"publication_date":"2011-02-18","ids":{"openalex":"https://openalex.org/W2103641619","doi":"https://doi.org/10.1109/tit.2011.2104670","mag":"2103641619"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2104670","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2104670","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/0909.2234","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039592314","display_name":"Jayakrishnan Unnikrishnan","orcid":"https://orcid.org/0000-0002-8464-4641"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["CH","US"],"is_corresponding":true,"raw_author_name":"Jayakrishnan Unnikrishnan","raw_affiliation_strings":["Audiovisual Communications Laboratory, Swiss Federal Institute of Technology, Lausanne, Switzerland","Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Audiovisual Communications Laboratory, Swiss Federal Institute of Technology, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115621193","display_name":"Dayu Huang","orcid":"https://orcid.org/0009-0009-3267-3799"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dayu Huang","raw_affiliation_strings":["Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047988825","display_name":"Sean Meyn","orcid":"https://orcid.org/0000-0002-8558-365X"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sean P. Meyn","raw_affiliation_strings":["Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054958460","display_name":"Amit Surana","orcid":"https://orcid.org/0000-0002-6409-5139"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amit Surana","raw_affiliation_strings":["United Technologies Research Center, Inc., East Hartford, CT, USA"],"affiliations":[{"raw_affiliation_string":"United Technologies Research Center, Inc., East Hartford, CT, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067089715","display_name":"Venugopal V. Veeravalli","orcid":"https://orcid.org/0000-0001-5490-0037"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Venugopal V. Veeravalli","raw_affiliation_strings":["Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5039592314"],"corresponding_institution_ids":["https://openalex.org/I157725225","https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":5.3863,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.96281075,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"57","issue":"3","first_page":"1587","last_page":"1603"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.995199978351593,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.995199978351593,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.994700014591217,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.7714852094650269},{"id":"https://openalex.org/keywords/null-distribution","display_name":"Null distribution","score":0.6965881586074829},{"id":"https://openalex.org/keywords/test-statistic","display_name":"Test statistic","score":0.6453325152397156},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.6422744989395142},{"id":"https://openalex.org/keywords/statistical-hypothesis-testing","display_name":"Statistical hypothesis testing","score":0.6193069219589233},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.5904183387756348},{"id":"https://openalex.org/keywords/one-and-two-tailed-tests","display_name":"One- and two-tailed tests","score":0.5668071508407593},{"id":"https://openalex.org/keywords/alternative-hypothesis","display_name":"Alternative hypothesis","score":0.5246896147727966},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5159645676612854},{"id":"https://openalex.org/keywords/null-hypothesis","display_name":"Null hypothesis","score":0.5074750781059265},{"id":"https://openalex.org/keywords/exponential-family","display_name":"Exponential family","score":0.4605637192726135},{"id":"https://openalex.org/keywords/likelihood-ratio-test","display_name":"Likelihood-ratio test","score":0.4540650248527527},{"id":"https://openalex.org/keywords/f-test-of-equality-of-variances","display_name":"F-test of equality of variances","score":0.45078033208847046},{"id":"https://openalex.org/keywords/p-value","display_name":"p-value","score":0.43217408657073975},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4305141568183899},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.428869366645813},{"id":"https://openalex.org/keywords/z-test","display_name":"Z-test","score":0.4274396598339081},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.41776829957962036},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4143194854259491},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12271031737327576}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7714852094650269},{"id":"https://openalex.org/C120639","wikidata":"https://www.wikidata.org/wiki/Q7068958","display_name":"Null distribution","level":4,"score":0.6965881586074829},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.6453325152397156},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.6422744989395142},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.6193069219589233},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.5904183387756348},{"id":"https://openalex.org/C134742768","wikidata":"https://www.wikidata.org/wiki/Q7092298","display_name":"One- and two-tailed tests","level":5,"score":0.5668071508407593},{"id":"https://openalex.org/C120577422","wikidata":"https://www.wikidata.org/wiki/Q843558","display_name":"Alternative hypothesis","level":3,"score":0.5246896147727966},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5159645676612854},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.5074750781059265},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.4605637192726135},{"id":"https://openalex.org/C9483764","wikidata":"https://www.wikidata.org/wiki/Q585740","display_name":"Likelihood-ratio test","level":2,"score":0.4540650248527527},{"id":"https://openalex.org/C29447264","wikidata":"https://www.wikidata.org/wiki/Q5423649","display_name":"F-test of equality of variances","level":4,"score":0.45078033208847046},{"id":"https://openalex.org/C44036329","wikidata":"https://www.wikidata.org/wiki/Q253255","display_name":"p-value","level":3,"score":0.43217408657073975},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4305141568183899},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.428869366645813},{"id":"https://openalex.org/C117661179","wikidata":"https://www.wikidata.org/wiki/Q897827","display_name":"Z-test","level":4,"score":0.4274396598339081},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.41776829957962036},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4143194854259491},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12271031737327576},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2011.2104670","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2104670","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:0909.2234","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0909.2234","pdf_url":"https://arxiv.org/pdf/0909.2234","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.246.7649","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.246.7649","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0909.2234v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.756.2360","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.756.2360","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0909.2234.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0909.2234","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0909.2234","pdf_url":"https://arxiv.org/pdf/0909.2234","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":[{"score":0.6399999856948853,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1582655262","https://openalex.org/W1603443343","https://openalex.org/W1991315500","https://openalex.org/W2019841176","https://openalex.org/W2020428052","https://openalex.org/W2026274373","https://openalex.org/W2037376728","https://openalex.org/W2055309977","https://openalex.org/W2055480857","https://openalex.org/W2080514151","https://openalex.org/W2101131861","https://openalex.org/W2126178628","https://openalex.org/W2127904409","https://openalex.org/W2135293293","https://openalex.org/W2136144249","https://openalex.org/W2139761901","https://openalex.org/W2156950870","https://openalex.org/W2157619393","https://openalex.org/W2160570986","https://openalex.org/W2163154558","https://openalex.org/W2166944917","https://openalex.org/W2253476304","https://openalex.org/W2401632103","https://openalex.org/W2802739963","https://openalex.org/W3027327446","https://openalex.org/W3106344614","https://openalex.org/W4243316134","https://openalex.org/W4246098931","https://openalex.org/W4293404332"],"related_works":["https://openalex.org/W2018490949","https://openalex.org/W2503526006","https://openalex.org/W2185462963","https://openalex.org/W2071030262","https://openalex.org/W2035871637","https://openalex.org/W2141645866","https://openalex.org/W2040651120","https://openalex.org/W2421517780","https://openalex.org/W1998102414","https://openalex.org/W4255702486"],"abstract_inverted_index":{"For":[0,125],"the":[1,7,13,29,46,50,53,72,78,95,98,119,129,137,141,145,161,181,189,210,213,217,222],"universal":[2,26,33],"hypothesis":[3,16,55,122],"testing":[4,123],"problem,":[5],"where":[6,97],"goal":[8],"is":[9,65,85,115,133,159,163,177,207],"to":[10,76,87,118,209],"decide":[11],"between":[12,45],"known":[14],"null":[15,54,223],"distribution":[17,48,100,169],"and":[18,52,140],"some":[19],"other":[20],"unknown":[21],"distribution,":[22,131],"Hoeffding":[23,138,190],"proposed":[24],"a":[25,60,69,89,103,110,116,167,185],"test":[27,34,64,84,92,139,143,183,191,219],"in":[28,39,102,149,165,172,192,212],"nineteen":[30],"sixties.":[31],"Hoeffding's":[32,63],"statistic":[35],"can":[36],"be":[37,88],"written":[38],"terms":[40,150,193],"of":[41,49,62,71,106,128,151,156,194,216],"Kullback-Leibler":[42],"(K-L)":[43],"divergence":[44],"empirical":[47],"observations":[51],"distribution.":[56],"In":[57],"this":[58,157],"paper":[59],"modification":[61],"considered":[66],"based":[67],"on":[68],"relaxation":[70],"K-L":[73],"divergence,":[74],"referred":[75],"as":[77],"mismatched":[79,83,142,182],"divergence.":[80],"The":[81],"resulting":[82],"shown":[86,134,179],"generalized":[90],"likelihood-ratio":[91],"(GLRT)":[93],"for":[94,199],"case":[96],"alternate":[99,130],"lies":[101],"parametric":[104],"family":[105],"distributions":[107],"characterized":[108],"by":[109],"finite-dimensional":[111],"parameter,":[112],"i.e.,":[113],"it":[114,132],"solution":[117],"corresponding":[120],"composite":[121],"problem.":[124],"certain":[126],"choices":[127],"that":[135,160,180],"both":[136],"have":[144],"same":[146],"asymptotic":[147,214],"performance":[148,198],"error":[152],"exponents.":[153],"A":[154],"consequence":[155],"result":[158],"GLRT":[162],"optimal":[164],"differentiating":[166],"particular":[168],"from":[170],"others":[171],"an":[173],"exponential":[174],"family.":[175],"It":[176],"also":[178],"has":[184],"significant":[186],"advantage":[187,206],"over":[188],"finite":[195],"sample":[196],"size":[197],"applications":[200],"involving":[201],"large":[202],"alphabet":[203],"distributions.":[204],"This":[205],"due":[208],"difference":[211],"variances":[215],"two":[218],"statistics":[220],"under":[221],"hypothesis.":[224]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}