{"id":"https://openalex.org/W4307265281","doi":"https://doi.org/10.3390/sym14112227","title":"Reproducing Kernel Hilbert Space Approach to Multiresponse Smoothing Spline Regression Function","display_name":"Reproducing Kernel Hilbert Space Approach to Multiresponse Smoothing Spline Regression Function","publication_year":2022,"publication_date":"2022-10-23","ids":{"openalex":"https://openalex.org/W4307265281","doi":"https://doi.org/10.3390/sym14112227"},"language":"en","primary_location":{"id":"doi:10.3390/sym14112227","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14112227","pdf_url":"https://www.mdpi.com/2073-8994/14/11/2227/pdf?version=1667380993","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/11/2227/pdf?version=1667380993","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110825437","display_name":"Budi Lestari","orcid":null},"institutions":[{"id":"https://openalex.org/I205133468","display_name":"Airlangga University","ror":"https://ror.org/04ctejd88","country_code":"ID","type":"education","lineage":["https://openalex.org/I205133468"]},{"id":"https://openalex.org/I3129486149","display_name":"Universitas Jember","ror":"https://ror.org/049f0ha78","country_code":"ID","type":"education","lineage":["https://openalex.org/I3129486149"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Budi Lestari","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Natural Sciences, The University of Jember, Jember 68121, Indonesia","Research Group of Statistical Modeling in Life Sciences, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, The University of Jember, Jember 68121, Indonesia","institution_ids":["https://openalex.org/I3129486149"]},{"raw_affiliation_string":"Research Group of Statistical Modeling in Life Sciences, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia","institution_ids":["https://openalex.org/I205133468"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025506617","display_name":"Nur Chamidah","orcid":"https://orcid.org/0000-0003-1592-4671"},"institutions":[{"id":"https://openalex.org/I205133468","display_name":"Airlangga University","ror":"https://ror.org/04ctejd88","country_code":"ID","type":"education","lineage":["https://openalex.org/I205133468"]}],"countries":["ID"],"is_corresponding":true,"raw_author_name":"Nur Chamidah","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia","Research Group of Statistical Modeling in Life Sciences, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia"],"raw_orcid":"https://orcid.org/0000-0003-1592-4671","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia","institution_ids":["https://openalex.org/I205133468"]},{"raw_affiliation_string":"Research Group of Statistical Modeling in Life Sciences, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia","institution_ids":["https://openalex.org/I205133468"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083004617","display_name":"Dursun Ayd\u0131n","orcid":"https://orcid.org/0000-0001-8393-1270"},"institutions":[{"id":"https://openalex.org/I79946792","display_name":"Mu\u011fla University","ror":"https://ror.org/05n2cz176","country_code":"TR","type":"education","lineage":["https://openalex.org/I79946792"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Dursun Aydin","raw_affiliation_strings":["Department of Statistics, Faculty of Science, Mu\u011fla S\u0131tk\u0131 Ko\u00e7man University, Mu\u011fla 48000, Turkey"],"raw_orcid":"https://orcid.org/0000-0001-8393-1270","affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Science, Mu\u011fla S\u0131tk\u0131 Ko\u00e7man University, Mu\u011fla 48000, Turkey","institution_ids":["https://openalex.org/I79946792"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039626539","display_name":"Ersin Y\u0131lmaz","orcid":"https://orcid.org/0000-0002-9871-4700"},"institutions":[{"id":"https://openalex.org/I79946792","display_name":"Mu\u011fla University","ror":"https://ror.org/05n2cz176","country_code":"TR","type":"education","lineage":["https://openalex.org/I79946792"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Ersin Yilmaz","raw_affiliation_strings":["Department of Statistics, Faculty of Science, Mu\u011fla S\u0131tk\u0131 Ko\u00e7man University, Mu\u011fla 48000, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-9871-4700","affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Science, Mu\u011fla S\u0131tk\u0131 Ko\u00e7man University, Mu\u011fla 48000, Turkey","institution_ids":["https://openalex.org/I79946792"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025506617"],"corresponding_institution_ids":["https://openalex.org/I205133468"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.8489,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.92299316,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"14","issue":"11","first_page":"2227","last_page":"2227"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.996999979019165,"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":0.996999979019165,"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":0.9732999801635742,"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":0.9703999757766724,"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/nonparametric-regression","display_name":"Nonparametric regression","score":0.7117223143577576},{"id":"https://openalex.org/keywords/semiparametric-regression","display_name":"Semiparametric regression","score":0.6404722332954407},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5656999349594116},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5540680289268494},{"id":"https://openalex.org/keywords/smoothing-spline","display_name":"Smoothing spline","score":0.5303600430488586},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5193568468093872},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.5141575336456299},{"id":"https://openalex.org/keywords/kernel-smoother","display_name":"Kernel smoother","score":0.45248347520828247},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.4463811218738556},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.43556737899780273},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.4256367087364197},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35374557971954346},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3394334316253662},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.31513816118240356},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.171511709690094},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.15369799733161926},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.13287609815597534},{"id":"https://openalex.org/keywords/radial-basis-function-kernel","display_name":"Radial basis function kernel","score":0.08604875206947327},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.07806113362312317}],"concepts":[{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.7117223143577576},{"id":"https://openalex.org/C19539793","wikidata":"https://www.wikidata.org/wiki/Q7449609","display_name":"Semiparametric regression","level":3,"score":0.6404722332954407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5656999349594116},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5540680289268494},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.5303600430488586},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5193568468093872},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.5141575336456299},{"id":"https://openalex.org/C27406209","wikidata":"https://www.wikidata.org/wiki/Q6394203","display_name":"Kernel smoother","level":5,"score":0.45248347520828247},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.4463811218738556},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.43556737899780273},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.4256367087364197},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35374557971954346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3394334316253662},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.31513816118240356},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.171511709690094},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.15369799733161926},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.13287609815597534},{"id":"https://openalex.org/C75866337","wikidata":"https://www.wikidata.org/wiki/Q7280263","display_name":"Radial basis function kernel","level":4,"score":0.08604875206947327},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.07806113362312317},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14112227","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14112227","pdf_url":"https://www.mdpi.com/2073-8994/14/11/2227/pdf?version=1667380993","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:87e51660ff454e79a7603d16baafc5c9","is_oa":true,"landing_page_url":"https://doaj.org/article/87e51660ff454e79a7603d16baafc5c9","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":"Symmetry, Vol 14, Iss 11, p 2227 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/11/2227/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14112227","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14112227","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14112227","pdf_url":"https://www.mdpi.com/2073-8994/14/11/2227/pdf?version=1667380993","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2975282827","display_name":null,"funder_award_id":"PT/2022","funder_id":"https://openalex.org/F4320331994","funder_display_name":"Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi"},{"id":"https://openalex.org/G6007376380","display_name":null,"funder_award_id":"02.00.PT/2022","funder_id":"https://openalex.org/F4320331994","funder_display_name":"Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi"}],"funders":[{"id":"https://openalex.org/F4320325143","display_name":"Universitas Airlangga","ror":"https://ror.org/04ctejd88"},{"id":"https://openalex.org/F4320331994","display_name":"Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4307265281.pdf","grobid_xml":"https://content.openalex.org/works/W4307265281.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W1548450409","https://openalex.org/W1560724230","https://openalex.org/W1565176583","https://openalex.org/W1568892534","https://openalex.org/W1808447900","https://openalex.org/W1964429816","https://openalex.org/W1965590480","https://openalex.org/W1984338893","https://openalex.org/W1986280275","https://openalex.org/W1987515149","https://openalex.org/W1990420052","https://openalex.org/W2000175948","https://openalex.org/W2015904350","https://openalex.org/W2047091565","https://openalex.org/W2048706383","https://openalex.org/W2061599481","https://openalex.org/W2132904952","https://openalex.org/W2168029744","https://openalex.org/W2186844020","https://openalex.org/W2286642557","https://openalex.org/W2305315639","https://openalex.org/W2310233051","https://openalex.org/W2753631294","https://openalex.org/W2777382789","https://openalex.org/W2797333853","https://openalex.org/W2896482050","https://openalex.org/W2907590657","https://openalex.org/W2979564710","https://openalex.org/W2995142617","https://openalex.org/W2995518099","https://openalex.org/W2996360717","https://openalex.org/W3019737767","https://openalex.org/W3028982422","https://openalex.org/W3092812352","https://openalex.org/W3094322889","https://openalex.org/W3110746794","https://openalex.org/W3137444672","https://openalex.org/W3162196362","https://openalex.org/W3209957588","https://openalex.org/W4210785735","https://openalex.org/W4230615526","https://openalex.org/W4238717354","https://openalex.org/W4246311433","https://openalex.org/W4298876635","https://openalex.org/W4300000261","https://openalex.org/W4302599714","https://openalex.org/W4386877197","https://openalex.org/W6634048602","https://openalex.org/W6638474945","https://openalex.org/W6687186514","https://openalex.org/W6698345258","https://openalex.org/W6743942776","https://openalex.org/W6746693240","https://openalex.org/W6768701020","https://openalex.org/W6784827465","https://openalex.org/W6791361843","https://openalex.org/W6856207162"],"related_works":["https://openalex.org/W2996360717","https://openalex.org/W3137444672","https://openalex.org/W1991430094","https://openalex.org/W4236180998","https://openalex.org/W1559087056","https://openalex.org/W2462869830","https://openalex.org/W1808447900","https://openalex.org/W2896482050","https://openalex.org/W1562032116","https://openalex.org/W2494306148"],"abstract_inverted_index":{"In":[0,45,106,194],"statistical":[1,210],"analyses,":[2],"especially":[3,212],"those":[4],"using":[5,191],"a":[6,11,16,42,71,83,88,120,130,135,144,239],"multiresponse":[7,47,57,220,225,240],"regression":[8,43,49,58,62,112,173,222,227,242],"model":[9,13,51,127,243,246],"approach,":[10],"mathematical":[12],"that":[14,52,77],"describes":[15],"functional":[17],"relationship":[18,35],"between":[19,36,73],"more":[20,28],"than":[21],"one":[22,26],"response":[23],"variables":[24,30,38],"and":[25,133,163,167,224,229],"or":[27],"predictor":[29],"is":[31,39,53,70,79],"often":[32],"involved.":[33],"The":[34],"these":[37],"expressed":[40],"by":[41,129],"function.":[44],"the":[46,56,61,65,74,96,111,115,125,149,152,159,169,172,181,184,188,195,197,207,214,235],"nonparametric":[48,221,236],"(MNR)":[50],"part":[54],"of":[55,101,114,171,180,183,209,216,238],"model,":[59,117],"estimating":[60],"function":[63,113,174],"becomes":[64],"main":[66],"problem,":[67],"as":[68],"there":[69],"correlation":[72],"responses":[75],"such":[76],"it":[78],"necessary":[80],"to":[81,109,147,151,233,245],"include":[82],"symmetric":[84,160],"weight":[85,161],"matrix":[86,162],"into":[87],"penalized":[89],"weighted":[90],"least":[91],"square":[92],"(PWLS)":[93],"optimization":[94,122],"during":[95],"estimation":[97,189],"process.":[98],"This":[99],"is,":[100],"course,":[102],"very":[103],"complicated":[104],"mathematically.":[105],"this":[107,201],"study,":[108],"estimate":[110,234],"MNR":[116,126],"we":[118,157],"developed":[119,153,205],"PWLS":[121,154],"method":[123],"for":[124,187,213],"proposed":[128],"previous":[131],"researcher,":[132],"used":[134,232,244],"reproducing":[136],"kernel":[137],"Hilbert":[138],"space":[139],"(RKHS)":[140],"approach":[141],"based":[142],"on":[143],"smoothing":[145,165,185],"spline":[146],"obtain":[148],"solution":[150],"optimization.":[155],"Additionally,":[156],"determined":[158],"optimal":[164],"parameter,":[166],"investigated":[168],"consistency":[170],"estimator.":[175],"We":[176],"provide":[177],"an":[178],"illustration":[179],"effects":[182],"parameters":[186],"results":[190],"simulation":[192],"data.":[193],"future,":[196],"theory":[198],"generated":[199],"from":[200],"study":[202],"can":[203,230],"be":[204,231],"within":[206],"scope":[208],"inference,":[211],"purpose":[215],"testing":[217],"hypotheses":[218],"involving":[219],"models":[223],"semiparametric":[226,241],"models,":[228],"component":[237],"Indonesian":[247],"toddlers\u2019":[248],"standard":[249],"growth":[250],"charts.":[251]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}