{"id":"https://openalex.org/W4381686065","doi":"https://doi.org/10.3390/axioms12070613","title":"Scalar-on-Function Relative Error Regression for Weak Dependent Case","display_name":"Scalar-on-Function Relative Error Regression for Weak Dependent Case","publication_year":2023,"publication_date":"2023-06-21","ids":{"openalex":"https://openalex.org/W4381686065","doi":"https://doi.org/10.3390/axioms12070613"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12070613","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070613","pdf_url":"https://www.mdpi.com/2075-1680/12/7/613/pdf?version=1687332334","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/7/613/pdf?version=1687332334","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036984726","display_name":"Zouaoui Chikr Elmezouar","orcid":"https://orcid.org/0000-0001-7621-6711"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Zouaoui Chikr Elmezouar","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041542650","display_name":"Fatimah Alshahrani","orcid":"https://orcid.org/0000-0003-1306-7688"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fatimah Alshahrani","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038360872","display_name":"Ibrahim M. Almanjahie","orcid":"https://orcid.org/0000-0002-4651-3210"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ibrahim M. Almanjahie","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014732531","display_name":"Zoulikha Kaid","orcid":"https://orcid.org/0000-0002-9684-1589"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Zoulikha Kaid","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051329139","display_name":"Ali Laksaci","orcid":"https://orcid.org/0000-0001-6527-5783"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ali Laksaci","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079488129","display_name":"Mustapha Rachdi","orcid":"https://orcid.org/0000-0002-9203-056X"},"institutions":[{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mustapha Rachdi","raw_affiliation_strings":["Laboratory AGEIS, University of Grenoble Alpes, UFR SHS, BP. 47, Cedex 09, F38040 Grenoble, France"],"affiliations":[{"raw_affiliation_string":"Laboratory AGEIS, University of Grenoble Alpes, UFR SHS, BP. 47, Cedex 09, F38040 Grenoble, France","institution_ids":["https://openalex.org/I899635006"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5079488129"],"corresponding_institution_ids":["https://openalex.org/I899635006"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.3388,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.61437943,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"12","issue":"7","first_page":"613","last_page":"613"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","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/T10136","display_name":"Statistical Methods and Inference","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/T11236","display_name":"Control Systems and Identification","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9951000213623047,"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":0.760662317276001},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7300354838371277},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6542165279388428},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5648815631866455},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5616121292114258},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5558451414108276},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5108620524406433},{"id":"https://openalex.org/keywords/kernel-regression","display_name":"Kernel regression","score":0.5091409087181091},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.5025169849395752},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.5023293495178223},{"id":"https://openalex.org/keywords/kernel-smoother","display_name":"Kernel smoother","score":0.4954887628555298},{"id":"https://openalex.org/keywords/nonparametric-regression","display_name":"Nonparametric regression","score":0.4901596009731293},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4565325677394867},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4218020737171173},{"id":"https://openalex.org/keywords/regression-function","display_name":"Regression function","score":0.42117446660995483},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.34019291400909424},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.2275732457637787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17872563004493713},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1260133683681488},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12272030115127563},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.07832860946655273}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.760662317276001},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7300354838371277},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6542165279388428},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5648815631866455},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5616121292114258},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5558451414108276},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5108620524406433},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.5091409087181091},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.5025169849395752},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5023293495178223},{"id":"https://openalex.org/C27406209","wikidata":"https://www.wikidata.org/wiki/Q6394203","display_name":"Kernel smoother","level":5,"score":0.4954887628555298},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.4901596009731293},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4565325677394867},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4218020737171173},{"id":"https://openalex.org/C2988035592","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression function","level":3,"score":0.42117446660995483},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.34019291400909424},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.2275732457637787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17872563004493713},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1260133683681488},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12272030115127563},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.07832860946655273},{"id":"https://openalex.org/C75866337","wikidata":"https://www.wikidata.org/wiki/Q7280263","display_name":"Radial basis function kernel","level":4,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms12070613","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070613","pdf_url":"https://www.mdpi.com/2075-1680/12/7/613/pdf?version=1687332334","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04837604v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04837604","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, 2023, 12 (7), pp.613. &#x27E8;10.3390/axioms12070613&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:77c1aef31f9142e19e7572c7bd333675","is_oa":true,"landing_page_url":"https://doaj.org/article/77c1aef31f9142e19e7572c7bd333675","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 7, p 613 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/7/613/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12070613","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":"Axioms; Volume 12; Issue 7; Pages: 613","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12070613","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070613","pdf_url":"https://www.mdpi.com/2075-1680/12/7/613/pdf?version=1687332334","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"},{"id":"https://openalex.org/F4320337220","display_name":"Deanship of Scientific Research, Princess Nourah Bint Abdulrahman University","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4381686065.pdf"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1925137896","https://openalex.org/W1964341604","https://openalex.org/W1969842547","https://openalex.org/W1987334466","https://openalex.org/W1993834205","https://openalex.org/W2008353574","https://openalex.org/W2008996255","https://openalex.org/W2055710947","https://openalex.org/W2081797450","https://openalex.org/W2202191623","https://openalex.org/W2212329321","https://openalex.org/W2314066266","https://openalex.org/W2831911354","https://openalex.org/W2903456956","https://openalex.org/W2963503003","https://openalex.org/W3214110022","https://openalex.org/W4213371211","https://openalex.org/W4286628871","https://openalex.org/W6652126406","https://openalex.org/W6726842192","https://openalex.org/W6803383548"],"related_works":["https://openalex.org/W4241084170","https://openalex.org/W1984844694","https://openalex.org/W1808447900","https://openalex.org/W4295314470","https://openalex.org/W2370679488","https://openalex.org/W2608448015","https://openalex.org/W2482318124","https://openalex.org/W254163559","https://openalex.org/W4236180998","https://openalex.org/W1251986303"],"abstract_inverted_index":{"Analyzing":[0],"the":[1,4,8,20,24,38,47,53,64,69,96,101,112,115],"co-variability":[2],"between":[3],"Hilbert":[5],"regressor":[6],"and":[7,61,118],"scalar":[9],"output":[10],"variable":[11],"is":[12,29,86,108],"crucial":[13],"in":[14,81,121],"functional":[15,82],"statistics.":[16],"In":[17],"this":[18,33,75],"contribution,":[19],"kernel":[21],"smoothing":[22,97],"of":[23,46,68,74,114],"Relative":[25],"Error":[26],"Regression":[27],"(RE-regression)":[28],"used":[30],"to":[31,42,58,110],"resolve":[32],"problem.":[34],"Precisely,":[35],"we":[36,62,89],"use":[37],"relative":[39],"square":[40],"error":[41],"establish":[43],"an":[44,105],"estimator":[45],"Hilbertian":[48,54,76],"regression.":[49],"As":[50],"asymptotic":[51],"results,":[52],"observations":[55],"are":[56],"assumed":[57],"be":[59],"quasi-associated,":[60],"demonstrate":[63],"almost":[65],"complete":[66],"consistency":[67],"constructed":[70],"estimator.":[71],"The":[72],"feasibility":[73],"model":[77],"as":[78],"a":[79],"predictor":[80],"time":[83],"series":[84],"data":[85],"discussed.":[87],"Moreover,":[88],"give":[90],"some":[91],"practical":[92],"ideas":[93],"for":[94],"selecting":[95],"parameter":[98],"based":[99],"on":[100],"bootstrap":[102],"procedure.":[103],"Finally,":[104],"empirical":[106],"investigation":[107],"performed":[109],"examine":[111],"behavior":[113],"RE-regression":[116],"estimation":[117],"its":[119],"superiority":[120],"practice.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2023-06-23T00:00:00"}
