{"id":"https://openalex.org/W2808564496","doi":"https://doi.org/10.3390/e20060464","title":"Non-Quadratic Distances in Model Assessment","display_name":"Non-Quadratic Distances in Model Assessment","publication_year":2018,"publication_date":"2018-06-14","ids":{"openalex":"https://openalex.org/W2808564496","doi":"https://doi.org/10.3390/e20060464","mag":"2808564496","pmid":"https://pubmed.ncbi.nlm.nih.gov/33265554"},"language":"en","primary_location":{"id":"doi:10.3390/e20060464","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20060464","pdf_url":"https://www.mdpi.com/1099-4300/20/6/464/pdf?version=1528979209","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/20/6/464/pdf?version=1528979209","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009202015","display_name":"Marianthi Markatou","orcid":"https://orcid.org/0000-0002-1453-8229"},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Marianthi Markatou","raw_affiliation_strings":["Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA"],"raw_orcid":"https://orcid.org/0000-0002-1453-8229","affiliations":[{"raw_affiliation_string":"Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA","institution_ids":["https://openalex.org/I63190737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100350409","display_name":"Yang Chen","orcid":"https://orcid.org/0000-0002-1928-2381"},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yang Chen","raw_affiliation_strings":["Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA"],"raw_orcid":"https://orcid.org/0000-0002-1928-2381","affiliations":[{"raw_affiliation_string":"Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA","institution_ids":["https://openalex.org/I63190737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009202015"],"corresponding_institution_ids":["https://openalex.org/I63190737"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.9502,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87821799,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"20","issue":"6","first_page":"464","last_page":"464"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9927999973297119,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9927999973297119,"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":0.9894999861717224,"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/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.651104211807251},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5747488737106323},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5650641322135925},{"id":"https://openalex.org/keywords/model-selection","display_name":"Model selection","score":0.5577876567840576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5467948913574219},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.460172563791275},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.45246222615242004},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.43499869108200073},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.4305422306060791},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4296906292438507},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4130456745624542},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.35710960626602173},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.34402453899383545},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32283738255500793},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2748962640762329}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.651104211807251},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5747488737106323},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5650641322135925},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.5577876567840576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5467948913574219},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.460172563791275},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.45246222615242004},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.43499869108200073},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.4305422306060791},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4296906292438507},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4130456745624542},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.35710960626602173},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.34402453899383545},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32283738255500793},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2748962640762329},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e20060464","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20060464","pdf_url":"https://www.mdpi.com/1099-4300/20/6/464/pdf?version=1528979209","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":"pmid:33265554","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33265554","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:1f5038193d8b4ce6a8d803cc13661f1a","is_oa":true,"landing_page_url":"https://doaj.org/article/1f5038193d8b4ce6a8d803cc13661f1a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 20, Iss 6, p 464 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/20/6/464/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20060464","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","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7512982","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7512982","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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 (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e20060464","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20060464","pdf_url":"https://www.mdpi.com/1099-4300/20/6/464/pdf?version=1528979209","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":[{"score":0.5,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2808564496.pdf","grobid_xml":"https://content.openalex.org/works/W2808564496.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W41562140","https://openalex.org/W240730124","https://openalex.org/W603661147","https://openalex.org/W1487839521","https://openalex.org/W1516900628","https://openalex.org/W1965555277","https://openalex.org/W1969570435","https://openalex.org/W1977163402","https://openalex.org/W1978456583","https://openalex.org/W1983874989","https://openalex.org/W2006228748","https://openalex.org/W2008567788","https://openalex.org/W2009146966","https://openalex.org/W2028644998","https://openalex.org/W2033468335","https://openalex.org/W2048090396","https://openalex.org/W2053754561","https://openalex.org/W2081462278","https://openalex.org/W2081812284","https://openalex.org/W2096868992","https://openalex.org/W2117274097","https://openalex.org/W2117890631","https://openalex.org/W2130019680","https://openalex.org/W2137195100","https://openalex.org/W2142635246","https://openalex.org/W2144553591","https://openalex.org/W2169014752","https://openalex.org/W2479315779","https://openalex.org/W2754184402","https://openalex.org/W2783606607","https://openalex.org/W2789861755","https://openalex.org/W2905764853","https://openalex.org/W3102178621","https://openalex.org/W3104989738","https://openalex.org/W3105391667","https://openalex.org/W4210855551","https://openalex.org/W4248962116","https://openalex.org/W4250877794"],"related_works":["https://openalex.org/W2386430105","https://openalex.org/W2356521405","https://openalex.org/W2038534795","https://openalex.org/W2384358604","https://openalex.org/W1567829292","https://openalex.org/W2041845946","https://openalex.org/W2113107995","https://openalex.org/W1966038674","https://openalex.org/W1607827294","https://openalex.org/W2895680438"],"abstract_inverted_index":{"One":[0],"natural":[1],"way":[2],"to":[3,21,50,120],"measure":[4],"model":[5,47,52,105],"adequacy":[6,44],"is":[7,19,124],"by":[8],"using":[9],"statistical":[10,61],"distances":[11,37],"as":[12,102],"loss":[13,23],"functions.":[14],"A":[15,107],"related":[16],"fundamental":[17],"question":[18],"how":[20],"construct":[22],"functions":[24],"that":[25,95],"are":[26,81],"scientifically":[27],"and":[28,38,63,77,92,117],"statistically":[29],"meaningful.":[30],"In":[31],"this":[32],"paper,":[33],"we":[34],"investigate":[35],"non-quadratic":[36],"their":[39,90,100,118],"role":[40],"in":[41,83],"assessing":[42],"the":[43,57,72,78,86,112],"of":[45,59,75,88,104,114],"a":[46,60],"and/or":[48],"ability":[49],"perform":[51],"selection.":[53],"We":[54],"first":[55],"present":[56],"definition":[58],"distance":[62],"its":[64],"associated":[65],"properties.":[66],"Three":[67],"popular":[68],"distances,":[69],"total":[70],"variation,":[71],"mixture":[73],"index":[74],"fit":[76],"Kullback-Leibler":[79],"distance,":[80],"studied":[82],"detail,":[84],"with":[85],"aim":[87],"understanding":[89],"properties":[91],"potential":[93],"interpretations":[94],"can":[96],"offer":[97],"insight":[98],"into":[99],"performance":[101,113],"measures":[103,116],"misspecification.":[106],"small":[108],"simulation":[109],"study":[110],"exemplifies":[111],"these":[115],"application":[119],"different":[121],"scientific":[122],"fields":[123],"briefly":[125],"discussed.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
