{"id":"https://openalex.org/W7215132902","doi":"https://doi.org/10.13140/rg.2.2.11409.80481","title":"Bias-Corrected Estimators for Joint Entropy, Conditional Entropy, and Mutual Information in the Discrete Bivariate Case: Theory and an Application to Motor Insurance","display_name":"Bias-Corrected Estimators for Joint Entropy, Conditional Entropy, and Mutual Information in the Discrete Bivariate Case: Theory and an Application to Motor Insurance","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7215132902","doi":"https://doi.org/10.13140/rg.2.2.11409.80481"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02558","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02558","pdf_url":"https://arxiv.org/pdf/2610.02558","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.02558","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055479037","display_name":"Amadou Diadi\u00e9 Ba","orcid":"https://orcid.org/0000-0003-0893-4951","observed_orcids":["https://orcid.org/0000-0003-0893-4951"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Amadou Diadi\u00e9 B\u00e2","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5055479037"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.9101999998092651,"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/T13500","display_name":"Probability and Statistical Research","score":0.9101999998092651,"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/T10136","display_name":"Statistical Methods and Inference","score":0.034699998795986176,"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/T13141","display_name":"Statistical Methods and Applications","score":0.021299999207258224,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/joint-entropy","display_name":"joint entropy","score":0.9369999766349792},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"conditional entropy","score":1.0},{"id":"https://openalex.org/keywords/mutual-information","display_name":"mutual information","score":1.0},{"id":"https://openalex.org/keywords/bias-correction","display_name":"bias correction","score":0.7599999904632568},{"id":"https://openalex.org/keywords/finite-sample-bias","display_name":"finite-sample bias","score":0.8080000281333923},{"id":"https://openalex.org/keywords/discrete-random-variables","display_name":"discrete random variables","score":0.8220000267028809},{"id":"https://openalex.org/keywords/plug-in-estimator","display_name":"plug-in estimator","score":0.8389999866485596},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"asymptotic distribution","score":0.8650000095367432},{"id":"https://openalex.org/keywords/independence-testing","display_name":"independence testing","score":0.8130000233650208},{"id":"https://openalex.org/keywords/wilks-theorem","display_name":"Wilks' theorem","score":0.9879999756813049},{"id":"https://openalex.org/keywords/auto-insurance","display_name":"automobile insurance","score":0.9300000071525574},{"id":"https://openalex.org/keywords/risk-classification","display_name":"risk classification","score":0.7950000166893005},{"id":"https://openalex.org/keywords/claim-severity","display_name":"claim severity","score":0.9990000128746033}],"concepts":[{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.7786999940872192},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6662999987602234},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.5806000232696533},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5687999725341797},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.5645999908447266},{"id":"https://openalex.org/C124805900","wikidata":"https://www.wikidata.org/wiki/Q5159269","display_name":"Conditional mutual information","level":3,"score":0.4975999891757965},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.45019999146461487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4325999915599823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.388700008392334},{"id":"https://openalex.org/C7797323","wikidata":"https://www.wikidata.org/wiki/Q3798612","display_name":"Pointwise mutual information","level":3,"score":0.38260000944137573},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.37459999322891235},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C113336015","wikidata":"https://www.wikidata.org/wiki/Q574010","display_name":"Complete information","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3125},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.258899986743927},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.251800000667572}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2610.02558","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02558","pdf_url":"https://arxiv.org/pdf/2610.02558","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.02558","doi":"https://doi.org/10.48550/arxiv.2610.02558","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02558","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.13140/rg.2.2.11409.80481","doi":"https://doi.org/10.13140/rg.2.2.11409.80481","is_oa":false,"landing_page_url":"https://doi.org/10.13140/rg.2.2.11409.80481","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02558","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02558","pdf_url":"https://arxiv.org/pdf/2610.02558","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215132902.pdf","grobid_xml":"https://content.openalex.org/works/W7215132902.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2999586361","https://openalex.org/W3006246550","https://openalex.org/W7203752441"],"related_works":["https://openalex.org/W7100364524","https://openalex.org/W2526273038","https://openalex.org/W2234332869","https://openalex.org/W2621318916","https://openalex.org/W3214323820","https://openalex.org/W2618001525","https://openalex.org/W2185272062","https://openalex.org/W7098265018","https://openalex.org/W2108657681","https://openalex.org/W7101195046"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,24,49,63,69,88,96,105,120,126,131,135],"finite-sample":[4],"bias":[5,37,136],"of":[6,82],"plug-in":[7],"estimators":[8,61],"for":[9,17,62,138],"joint":[10],"entropy,":[11,13],"conditional":[12],"and":[14,47,55,66,71,104,124],"mutual":[15],"information":[16],"finitely":[18],"supported":[19],"discrete":[20],"random":[21],"variables.":[22],"Using":[23],"univariate":[25],"reduction":[26],"framework":[27],"developed":[28],"in":[29],"our":[30],"companion":[31],"works,":[32],"we":[33],"derive":[34],"explicit":[35],"first-order":[36],"formulas.":[38],"For":[39],"a":[40,79,100,113],"pair":[41],"(X,Y)":[42],"with":[43,107],"support":[44],"sizes":[45],"r":[46],"s,":[48],"biases":[50],"are":[51,74],"respectively":[52],"-(rs-1)/(2n),":[53],"-r(s-1)/(2n),":[54],"(r-1)(s-1)/(2n).":[56],"We":[57],"then":[58],"propose":[59],"bias-corrected":[60],"three":[64],"measures":[65],"prove":[67],"that":[68],"uncorrected":[70],"corrected":[72],"versions":[73],"asymptotically":[75],"equivalent,":[76],"differing":[77],"by":[78,134],"deterministic":[80],"term":[81],"order":[83],"O(1/n);":[84],"consequently,":[85],"they":[86],"share":[87],"same":[89],"asymptotic":[90],"distribution.":[91],"A":[92],"simulation":[93],"study":[94,103],"validates":[95],"theoretical":[97],"results,":[98],"including":[99],"dedicated":[101],"independence":[102],"relationship":[106],"Wilks'":[108],"theorem.":[109],"An":[110],"application":[111],"to":[112],"motor":[114],"insurance":[115],"portfolio,":[116],"where":[117],"X":[118],"is":[119],"driver's":[121],"age":[122],"class":[123],"Y":[125],"claim":[127],"severity":[128],"class,":[129],"illustrates":[130],"improvement":[132],"brought":[133],"correction":[137],"risk":[139],"classification.":[140]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-02T00:00:00"}