{"id":"https://openalex.org/W1981637443","doi":"https://doi.org/10.3390/e16020921","title":"Statistical Analysis of Distance Estimators with Density Differences and Density Ratios","display_name":"Statistical Analysis of Distance Estimators with Density Differences and Density Ratios","publication_year":2014,"publication_date":"2014-02-17","ids":{"openalex":"https://openalex.org/W1981637443","doi":"https://doi.org/10.3390/e16020921","mag":"1981637443"},"language":"en","primary_location":{"id":"doi:10.3390/e16020921","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16020921","pdf_url":"https://www.mdpi.com/1099-4300/16/2/921/pdf?version=1424785291","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/16/2/921/pdf?version=1424785291","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088569462","display_name":"Takafumi Kanamori","orcid":"https://orcid.org/0000-0001-6878-5850"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]},{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takafumi Kanamori","raw_affiliation_strings":["Nagoya University, Furocho, Chikusaku, Nagoya 464-8603, Japan","Tokyo Inst. of Tech"],"raw_orcid":"https://orcid.org/0000-0001-6878-5850","affiliations":[{"raw_affiliation_string":"Nagoya University, Furocho, Chikusaku, Nagoya 464-8603, Japan","institution_ids":["https://openalex.org/I60134161"]},{"raw_affiliation_string":"Tokyo Inst. of Tech","institution_ids":["https://openalex.org/I114531698"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072744508","display_name":"Masashi Sugiyama","orcid":"https://orcid.org/0000-0001-6658-6743"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]},{"id":"https://openalex.org/I60134161","display_name":"Nagoya University","ror":"https://ror.org/04chrp450","country_code":"JP","type":"education","lineage":["https://openalex.org/I60134161"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masashi Sugiyama","raw_affiliation_strings":["Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan","#N##TAB##TAB##TAB##TAB# Nagoya University#N##TAB##TAB##TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan","institution_ids":["https://openalex.org/I114531698"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# Nagoya University#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I60134161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.3056,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.60289785,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"2","first_page":"921","last_page":"942"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9995999932289124,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9995999932289124,"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":0.9977999925613403,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9941999912261963,"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/mathematics","display_name":"Mathematics","score":0.7460553646087646},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7135632038116455},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.6831245422363281},{"id":"https://openalex.org/keywords/density-estimation","display_name":"Density estimation","score":0.6415224075317383},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.5775926113128662},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5673940777778625},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.518284022808075},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.47654062509536743},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4414401948451996},{"id":"https://openalex.org/keywords/kernel-density-estimation","display_name":"Kernel density estimation","score":0.41807055473327637},{"id":"https://openalex.org/keywords/statistical-distance","display_name":"Statistical distance","score":0.410494327545166},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37419602274894714},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3558894693851471},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14265021681785583},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10367172956466675},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07403382658958435}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7460553646087646},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7135632038116455},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6831245422363281},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.6415224075317383},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5775926113128662},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5673940777778625},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.518284022808075},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.47654062509536743},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4414401948451996},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.41807055473327637},{"id":"https://openalex.org/C58948655","wikidata":"https://www.wikidata.org/wiki/Q7604392","display_name":"Statistical distance","level":3,"score":0.410494327545166},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37419602274894714},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3558894693851471},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14265021681785583},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10367172956466675},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07403382658958435},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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":3,"locations":[{"id":"doi:10.3390/e16020921","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16020921","pdf_url":"https://www.mdpi.com/1099-4300/16/2/921/pdf?version=1424785291","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a80c6efb0173430e95f701e090b52020","is_oa":true,"landing_page_url":"https://doaj.org/article/a80c6efb0173430e95f701e090b52020","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 16, Iss 2, Pp 921-942 (2014)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/16/2/921/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e16020921","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 16; Issue 2; Pages: 921-942","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e16020921","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16020921","pdf_url":"https://www.mdpi.com/1099-4300/16/2/921/pdf?version=1424785291","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G836346074","display_name":"Theory and Applications of Density Ratio","funder_award_id":"24500340","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W91088564","https://openalex.org/W149129625","https://openalex.org/W149581298","https://openalex.org/W152055444","https://openalex.org/W1493730910","https://openalex.org/W1752120951","https://openalex.org/W1979804848","https://openalex.org/W1990970321","https://openalex.org/W2001854273","https://openalex.org/W2012712694","https://openalex.org/W2017116866","https://openalex.org/W2025720061","https://openalex.org/W2034368206","https://openalex.org/W2035641621","https://openalex.org/W2042179218","https://openalex.org/W2044688385","https://openalex.org/W2051670307","https://openalex.org/W2062291443","https://openalex.org/W2073241381","https://openalex.org/W2089394015","https://openalex.org/W2093951512","https://openalex.org/W2099111195","https://openalex.org/W2106579555","https://openalex.org/W2117381306","https://openalex.org/W2117890631","https://openalex.org/W2138449831","https://openalex.org/W2166944917","https://openalex.org/W2170935389","https://openalex.org/W3101108864","https://openalex.org/W3127518054","https://openalex.org/W4210855551","https://openalex.org/W4244473079","https://openalex.org/W4255230573","https://openalex.org/W4285719527","https://openalex.org/W6806599836"],"related_works":["https://openalex.org/W1482149696","https://openalex.org/W2351755528","https://openalex.org/W2977337932","https://openalex.org/W2465871978","https://openalex.org/W2144201579","https://openalex.org/W4240479520","https://openalex.org/W1528102763","https://openalex.org/W2585385340","https://openalex.org/W1569550976","https://openalex.org/W4297926828"],"abstract_inverted_index":{"Estimating":[0],"a":[1],"discrepancy":[2,24],"between":[3],"two":[4,21,53],"probability":[5,93,115],"distributions":[6],"from":[7],"samples":[8],"is":[9,55],"an":[10],"important":[11],"task":[12],"in":[13,95],"statistics":[14],"and":[15,37,59,106,126],"machine":[16],"learning.":[17],"There":[18],"are":[19,86],"mainly":[20],"classes":[22,54],"of":[23,51,92,123],"measures:":[25],"distance":[26],"measures":[27,39],"based":[28,40,66],"on":[29,41,67],"the":[30,35,42,47,56,68,72,82,90,103,107,121],"density":[31,43,69,73,104,108],"difference,":[32],"such":[33,45],"as":[34,46],"Lp-distances,":[36],"divergence":[38],"ratio,":[44],"\u03a6-divergences.":[48],"The":[49],"intersection":[50],"these":[52,124],"L1-distance":[57],"measure,":[58],"thus,":[60],"it":[61],"can":[62],"be":[63],"estimated":[64],"either":[65],"difference":[70,105],"or":[71],"ratio.":[74],"In":[75],"this":[76],"paper,":[77],"we":[78],"first":[79],"show":[80],"that":[81],"Bregman":[83],"scores,":[84],"which":[85],"widely":[87],"employed":[88],"for":[89],"estimation":[91],"densities":[94],"statistical":[96],"data":[97],"analysis,":[98],"allows":[99],"us":[100],"to":[101],"estimate":[102],"ratio":[109],"directly":[110],"without":[111],"separately":[112],"estimating":[113],"each":[114],"distribution.":[116],"We":[117],"then":[118],"theoretically":[119],"elucidate":[120],"robustness":[122],"estimators":[125],"present":[127],"numerical":[128],"experiments.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}