{"id":"https://openalex.org/W3009246797","doi":"https://doi.org/10.3390/e22030278","title":"Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models","display_name":"Statistical Generalized Derivative Applied to the Profile Likelihood Estimation in a Mixture of Semiparametric Models","publication_year":2020,"publication_date":"2020-02-28","ids":{"openalex":"https://openalex.org/W3009246797","doi":"https://doi.org/10.3390/e22030278","mag":"3009246797","pmid":"https://pubmed.ncbi.nlm.nih.gov/33286050"},"language":"en","primary_location":{"id":"doi:10.3390/e22030278","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22030278","pdf_url":"https://www.mdpi.com/1099-4300/22/3/278/pdf?version=1584696385","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/1099-4300/22/3/278/pdf?version=1584696385","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034569218","display_name":"Yuichi Hirose","orcid":"https://orcid.org/0000-0001-5565-3314"},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"education","lineage":["https://openalex.org/I41156924"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Yuichi Hirose","raw_affiliation_strings":["School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, 6140 Wellington, New Zealand"],"raw_orcid":"https://orcid.org/0000-0001-5565-3314","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, 6140 Wellington, New Zealand","institution_ids":["https://openalex.org/I41156924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083310167","display_name":"Ivy Liu","orcid":"https://orcid.org/0000-0002-3152-2632"},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"education","lineage":["https://openalex.org/I41156924"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Ivy Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, 6140 Wellington, New Zealand"],"raw_orcid":"https://orcid.org/0000-0002-3152-2632","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, 6140 Wellington, New Zealand","institution_ids":["https://openalex.org/I41156924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034569218"],"corresponding_institution_ids":["https://openalex.org/I41156924"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.4413,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63920778,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"22","issue":"3","first_page":"278","last_page":"278"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9994000196456909,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9994000196456909,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9958000183105469,"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"}},{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.993399977684021,"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/estimator","display_name":"Estimator","score":0.6498956680297852},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6394287347793579},{"id":"https://openalex.org/keywords/likelihood-function","display_name":"Likelihood function","score":0.5783146619796753},{"id":"https://openalex.org/keywords/estimating-equations","display_name":"Estimating equations","score":0.5427910685539246},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.5408362150192261},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5355320572853088},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5091201663017273},{"id":"https://openalex.org/keywords/generalized-estimating-equation","display_name":"Generalized estimating equation","score":0.4890619218349457},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4706909954547882},{"id":"https://openalex.org/keywords/semiparametric-regression","display_name":"Semiparametric regression","score":0.45270416140556335},{"id":"https://openalex.org/keywords/normality","display_name":"Normality","score":0.44389232993125916},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.4283408224582672},{"id":"https://openalex.org/keywords/score","display_name":"Score","score":0.42534926533699036},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42412546277046204}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6498956680297852},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6394287347793579},{"id":"https://openalex.org/C89106044","wikidata":"https://www.wikidata.org/wiki/Q45284","display_name":"Likelihood function","level":3,"score":0.5783146619796753},{"id":"https://openalex.org/C204016326","wikidata":"https://www.wikidata.org/wiki/Q5401384","display_name":"Estimating equations","level":3,"score":0.5427910685539246},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.5408362150192261},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5355320572853088},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5091201663017273},{"id":"https://openalex.org/C27403532","wikidata":"https://www.wikidata.org/wiki/Q5532474","display_name":"Generalized estimating equation","level":2,"score":0.4890619218349457},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4706909954547882},{"id":"https://openalex.org/C19539793","wikidata":"https://www.wikidata.org/wiki/Q7449609","display_name":"Semiparametric regression","level":3,"score":0.45270416140556335},{"id":"https://openalex.org/C2776157432","wikidata":"https://www.wikidata.org/wiki/Q1375683","display_name":"Normality","level":2,"score":0.44389232993125916},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.4283408224582672},{"id":"https://openalex.org/C65660741","wikidata":"https://www.wikidata.org/wiki/Q3952743","display_name":"Score","level":2,"score":0.42534926533699036},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42412546277046204},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e22030278","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22030278","pdf_url":"https://www.mdpi.com/1099-4300/22/3/278/pdf?version=1584696385","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:33286050","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33286050","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:4950fb58a6864a4a86b00a2adeff3209","is_oa":true,"landing_page_url":"https://doaj.org/article/4950fb58a6864a4a86b00a2adeff3209","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 22, Iss 3, p 278 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/22/3/278/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e22030278","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:7516731","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7516731","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/e22030278","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22030278","pdf_url":"https://www.mdpi.com/1099-4300/22/3/278/pdf?version=1584696385","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":0.4300000071525574,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G4055396756","display_name":null,"funder_award_id":"E2987-3648","funder_id":"https://openalex.org/F4320335369","funder_display_name":"Marsden Fund"},{"id":"https://openalex.org/G6531787488","display_name":null,"funder_award_id":"E2987-3648","funder_id":"https://openalex.org/F4320320774","funder_display_name":"Royal Society Te Ap\u0101rangi"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320320774","display_name":"Royal Society Te Ap\u0101rangi","ror":"https://ror.org/04tajb587"},{"id":"https://openalex.org/F4320335369","display_name":"Marsden Fund","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3009246797.pdf","grobid_xml":"https://content.openalex.org/works/W3009246797.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1222853772","https://openalex.org/W1460189015","https://openalex.org/W1967579825","https://openalex.org/W2001496329","https://openalex.org/W2010353172","https://openalex.org/W2012500654","https://openalex.org/W2021894274","https://openalex.org/W2034945547","https://openalex.org/W2085772899","https://openalex.org/W2086924664","https://openalex.org/W2124652134","https://openalex.org/W2133770727","https://openalex.org/W2401974674","https://openalex.org/W2466729165","https://openalex.org/W2977606681","https://openalex.org/W3104117975","https://openalex.org/W4240400659","https://openalex.org/W4367633674","https://openalex.org/W6712843461"],"related_works":["https://openalex.org/W188365466","https://openalex.org/W1994291014","https://openalex.org/W1604193326","https://openalex.org/W2117883387","https://openalex.org/W4299883198","https://openalex.org/W2545491858","https://openalex.org/W1998609512","https://openalex.org/W1977429167","https://openalex.org/W3194345457","https://openalex.org/W4250190209"],"abstract_inverted_index":{"There":[0],"is":[1,29,56],"a":[2],"difficulty":[3,28,47],"in":[4,18,39,70],"finding":[5],"an":[6,34],"estimate":[7],"of":[8,13,22,33,63,72],"the":[9,14,19,31,40,46,50,60,64,67,73],"standard":[10],"error":[11],"(SE)":[12],"profile":[15,41,74],"likelihood":[16,42,75],"estimator":[17,65],"joint":[20],"model":[21],"longitudinal":[23],"and":[24],"survival":[25],"data.":[26],"The":[27,54],"on":[30],"differentiation":[32],"implicit":[35],"function":[36],"that":[37],"appear":[38],"estimation.":[43],"We":[44],"solve":[45],"by":[48],"introducing":[49],"\"statistical":[51],"generalized":[52],"derivative\".":[53],"derivative":[55],"used":[57],"to":[58],"show":[59],"asymptotic":[61],"normality":[62],"with":[66],"SE":[68],"expressed":[69],"terms":[71],"score":[76],"function.":[77]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}