{"id":"https://openalex.org/W2131940723","doi":"https://doi.org/10.1109/tit.2006.881731","title":"On Divergences and Informations in Statistics and Information Theory","display_name":"On Divergences and Informations in Statistics and Information Theory","publication_year":2006,"publication_date":"2006-09-29","ids":{"openalex":"https://openalex.org/W2131940723","doi":"https://doi.org/10.1109/tit.2006.881731","mag":"2131940723"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2006.881731","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2006.881731","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/A5034116230","display_name":"Friedrich Liese","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"F. Liese","raw_affiliation_strings":["Dept. of Math., Rostock Univ"],"affiliations":[{"raw_affiliation_string":"Dept. of Math., Rostock Univ","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114033257","display_name":"Igor Vajda","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119419","display_name":"Czech Academy of Sciences, Institute of Information Theory and Automation","ror":"https://ror.org/03h1hsz49","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210119419"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"I. Vajda","raw_affiliation_strings":["[Institute of Information Theory andAutomation, Academy of Sciences\uc2a0of the\uc2a0Czech Republic, Prague, Czech Republic]"],"affiliations":[{"raw_affiliation_string":"[Institute of Information Theory andAutomation, Academy of Sciences\uc2a0of the\uc2a0Czech Republic, Prague, Czech Republic]","institution_ids":["https://openalex.org/I4210119419"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034116230"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.2699,"has_fulltext":false,"cited_by_count":597,"citation_normalized_percentile":{"value":0.98630985,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"52","issue":"10","first_page":"4394","last_page":"4412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9840999841690063,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9613000154495239,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/information-theory","display_name":"Information theory","score":0.642043948173523},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5439427495002747},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.45195358991622925},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3331988751888275},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32211291790008545}],"concepts":[{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.642043948173523},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5439427495002747},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.45195358991622925},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3331988751888275},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32211291790008545}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2006.881731","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2006.881731","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":[{"display_name":"Reduced inequalities","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W152055444","https://openalex.org/W638747377","https://openalex.org/W1505771370","https://openalex.org/W1531677953","https://openalex.org/W1535258871","https://openalex.org/W1549664537","https://openalex.org/W1552416095","https://openalex.org/W1560089794","https://openalex.org/W1965555277","https://openalex.org/W1969304434","https://openalex.org/W1973375658","https://openalex.org/W1985797129","https://openalex.org/W1993536789","https://openalex.org/W1995875735","https://openalex.org/W2000015806","https://openalex.org/W2017170340","https://openalex.org/W2042587503","https://openalex.org/W2049279961","https://openalex.org/W2063703901","https://openalex.org/W2076537505","https://openalex.org/W2077541600","https://openalex.org/W2081985429","https://openalex.org/W2099111195","https://openalex.org/W2101466250","https://openalex.org/W2107676886","https://openalex.org/W2116891837","https://openalex.org/W2122759946","https://openalex.org/W2122882636","https://openalex.org/W2126663884","https://openalex.org/W2130926302","https://openalex.org/W2132481658","https://openalex.org/W2138054245","https://openalex.org/W2146950091","https://openalex.org/W2149197198","https://openalex.org/W2149306165","https://openalex.org/W2158172508","https://openalex.org/W2159902206","https://openalex.org/W2160570986","https://openalex.org/W2161790804","https://openalex.org/W2163382065","https://openalex.org/W2164690070","https://openalex.org/W2174534725","https://openalex.org/W2320259161","https://openalex.org/W2396730238","https://openalex.org/W2797328151","https://openalex.org/W2947000318","https://openalex.org/W3127518054","https://openalex.org/W4213201159","https://openalex.org/W4294841944","https://openalex.org/W4297575875","https://openalex.org/W4300920051","https://openalex.org/W4301084947","https://openalex.org/W6679520213"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2225202932"],"abstract_inverted_index":{"The":[0,70,103,186],"paper":[1,138],"deals":[2],"with":[3,199],"the":[4,9,14,18,22,33,43,65,96,111,128,131,144,157,161,168,183,196,200,205,211,217],"f-divergences":[5,29,80,151],"of":[6,12,28,53,114,130,143,150,173,207],"Csiszar":[7],"generalizing":[8],"discrimination":[10],"information":[11,105,113],"Kullback,":[13],"total":[15],"variation":[16],"distance,":[17],"Hellinger":[19],"divergence,":[20],"and":[21,68,88,110,125,160,192,222],"Pearson":[23],"divergence.":[24],"All":[25],"basic":[26],"properties":[27,58],"including":[30],"relations":[31,63],"to":[32,64,118,123,167,179,216],"decision":[34],"errors":[35],"are":[36,59,81,116,152,177],"proved":[37,60],"in":[38,95,127,136,204],"a":[39,48],"new":[40,49,57,148],"manner":[41],"replacing":[42],"classical":[44,112,218],"Jensen":[45],"inequality":[46],"by":[47,107,141],"generalized":[50,71],"Taylor":[51,72],"expansion":[52,73],"convex":[54],"functions.":[55],"Some":[56,147],"too,":[61],"e.g.,":[62],"statistical":[66,83,104,190],"sufficiency":[67],"deficiency.":[69],"also":[74],"shows":[75],"very":[76],"easily":[77],"that":[78],"all":[79,174],"average":[82],"informations":[84],"(differences":[85],"between":[86],"prior":[87,101],"posterior":[89],"Bayes":[90],"errors)":[91],"mutually":[92],"differing":[93],"only":[94],"weights":[97],"imposed":[98],"on":[99,195],"various":[100],"distributions.":[102,209],"introduced":[106,135,153],"De":[108],"Groot":[109],"Shannon":[115,158,169],"shown":[117,178],"be":[119,180],"extremal":[120],"cases":[121],"corresponding":[122],"alpha=0":[124],"alpha=1":[126],"class":[129],"so-called":[132],"Arimoto":[133,145,162],"alpha-informations":[134],"this":[137,214],"for":[139,165],"0<alpha<1":[140],"means":[142],"alpha-entropies.":[146],"examples":[149],"as":[154],"well,":[155],"namely,":[156],"divergences":[159,176],"alpha-divergences":[163],"leading":[164],"alphauarr1":[166],"divergences.":[170],"Square":[171],"roots":[172],"these":[175],"metrics":[181],"satisfying":[182],"triangle":[184],"inequality.":[185],"last":[187],"section":[188],"introduces":[189],"tests":[191],"estimators":[193],"based":[194],"minimal":[197],"f-divergence":[198],"empirical":[201],"distribution":[202],"achieved":[203],"families":[206],"hypothetic":[208],"For":[210],"Kullback":[212],"divergence":[213],"leads":[215],"likelihood":[219],"ratio":[220],"test":[221],"estimator":[223]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":30},{"year":2023,"cited_by_count":37},{"year":2022,"cited_by_count":41},{"year":2021,"cited_by_count":61},{"year":2020,"cited_by_count":62},{"year":2019,"cited_by_count":48},{"year":2018,"cited_by_count":41},{"year":2017,"cited_by_count":33},{"year":2016,"cited_by_count":31},{"year":2015,"cited_by_count":28},{"year":2014,"cited_by_count":29},{"year":2013,"cited_by_count":25},{"year":2012,"cited_by_count":25}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
