{"id":"https://openalex.org/W4412083249","doi":"https://doi.org/10.3390/axioms14070516","title":"Exponential Squared Loss-Based Robust Variable Selection with Prior Information in Linear Regression Models","display_name":"Exponential Squared Loss-Based Robust Variable Selection with Prior Information in Linear Regression Models","publication_year":2025,"publication_date":"2025-07-04","ids":{"openalex":"https://openalex.org/W4412083249","doi":"https://doi.org/10.3390/axioms14070516"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14070516","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070516","pdf_url":"https://www.mdpi.com/2075-1680/14/7/516/pdf?version=1751627759","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/2075-1680/14/7/516/pdf?version=1751627759","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Hejun Wei","orcid":null},"institutions":[{"id":"https://openalex.org/I4210162190","display_name":"China University of Petroleum, East China","ror":"https://ror.org/05gbn2817","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210162190"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hejun Wei","raw_affiliation_strings":["College of Science, China University of Petroleum, Qingdao 266580, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, China University of Petroleum, Qingdao 266580, China","institution_ids":["https://openalex.org/I4210162190"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Tian Jin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210162190","display_name":"China University of Petroleum, East China","ror":"https://ror.org/05gbn2817","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210162190"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tian Jin","raw_affiliation_strings":["College of Science, China University of Petroleum, Qingdao 266580, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, China University of Petroleum, Qingdao 266580, China","institution_ids":["https://openalex.org/I4210162190"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100583281","display_name":"Yunquan Song","orcid":"https://orcid.org/0000-0002-4816-8588"},"institutions":[{"id":"https://openalex.org/I4210162190","display_name":"China University of Petroleum, East China","ror":"https://ror.org/05gbn2817","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210162190"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yunquan Song","raw_affiliation_strings":["College of Science, China University of Petroleum, Qingdao 266580, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, China University of Petroleum, Qingdao 266580, China","institution_ids":["https://openalex.org/I4210162190"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100583281"],"corresponding_institution_ids":["https://openalex.org/I4210162190"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14702283,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"7","first_page":"516","last_page":"516"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9991000294685364,"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":0.9991000294685364,"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":0.996999979019165,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9865000247955322,"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/linear-regression","display_name":"Linear regression","score":0.6254736185073853},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5895001292228699},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5154353380203247},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.4734625220298767},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4533322751522064},{"id":"https://openalex.org/keywords/feature-selection","display_name":"Feature selection","score":0.43847429752349854},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.42968106269836426},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.425533652305603},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3561413288116455},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28726476430892944}],"concepts":[{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.6254736185073853},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5895001292228699},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5154353380203247},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.4734625220298767},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4533322751522064},{"id":"https://openalex.org/C148483581","wikidata":"https://www.wikidata.org/wiki/Q446488","display_name":"Feature selection","level":2,"score":0.43847429752349854},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.42968106269836426},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.425533652305603},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3561413288116455},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28726476430892944},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14070516","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070516","pdf_url":"https://www.mdpi.com/2075-1680/14/7/516/pdf?version=1751627759","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:doaj.org/article:9e8079f425094f3a946258b45bca6382","is_oa":true,"landing_page_url":"https://doaj.org/article/9e8079f425094f3a946258b45bca6382","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":"Axioms, Vol 14, Iss 7, p 516 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14070516","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070516","pdf_url":"https://www.mdpi.com/2075-1680/14/7/516/pdf?version=1751627759","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":[{"id":"https://openalex.org/G48183633","display_name":null,"funder_award_id":"23CX03012A","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412083249.pdf","grobid_xml":"https://content.openalex.org/works/W4412083249.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1502338185","https://openalex.org/W1967819130","https://openalex.org/W1977777127","https://openalex.org/W1979216698","https://openalex.org/W2014453661","https://openalex.org/W2020925091","https://openalex.org/W2024046085","https://openalex.org/W2029469881","https://openalex.org/W2053061982","https://openalex.org/W2054640142","https://openalex.org/W2069627663","https://openalex.org/W2074682976","https://openalex.org/W2085448797","https://openalex.org/W2099396088","https://openalex.org/W2122825543","https://openalex.org/W2134056163","https://openalex.org/W2135046866","https://openalex.org/W2140514146","https://openalex.org/W2147534083","https://openalex.org/W2169103656","https://openalex.org/W2966241625","https://openalex.org/W2980187229","https://openalex.org/W3106348863","https://openalex.org/W4250589301","https://openalex.org/W6675338981","https://openalex.org/W6684653394"],"related_works":["https://openalex.org/W2102148524","https://openalex.org/W2314720829","https://openalex.org/W4385074335","https://openalex.org/W2575795810","https://openalex.org/W4400591661","https://openalex.org/W31220157","https://openalex.org/W2288557197","https://openalex.org/W4233024177","https://openalex.org/W2101914902","https://openalex.org/W3174613421"],"abstract_inverted_index":{"This":[0,109],"paper":[1,77,110],"proposes":[2],"a":[3,18,79,97,103,133],"robust":[4,80],"variable":[5,29,60],"selection":[6,61],"method":[7],"that":[8,87,139],"incorporates":[9],"prior":[10,50,64],"information":[11,51],"through":[12],"linear":[13,67],"constraints.":[14,68],"For":[15],"more":[16],"than":[17],"decade,":[19],"penalized":[20],"likelihood":[21],"frameworks":[22],"have":[23,96],"been":[24],"the":[25,71,88,107,112,118],"predominant":[26],"approach":[27],"for":[28],"selection,":[30],"where":[31],"appropriate":[32],"loss":[33,72,83],"and":[34,123,127,132],"penalty":[35],"functions":[36],"are":[37,102],"selected":[38],"to":[39,116,147],"formulate":[40],"unconstrained":[41],"optimization":[42],"problems.":[43],"However,":[44],"in":[45,75,106,151],"many":[46],"specific":[47],"applications,":[48],"some":[49,124],"can":[52],"be":[53],"obtained.":[54],"In":[55,69],"this":[56,76],"paper,":[57],"we":[58],"reformulate":[59],"by":[62],"incorporating":[63],"knowledge":[65],"as":[66],"addition,":[70],"function":[73],"adopted":[74],"is":[78],"exponential":[81],"squared":[82],"function,":[84],"which":[85],"ensures":[86],"estimation":[89,144],"of":[90,121],"model":[91,141],"parameter":[92],"coefficient":[93],"will":[94],"not":[95],"great":[98],"impact":[99],"when":[100],"there":[101],"few":[104],"outliers":[105],"dataset.":[108],"uses":[111],"designed":[113],"solution":[114],"algorithm":[115],"calculate":[117],"estimated":[119],"values":[120],"coefficients":[122],"other":[125],"parameters,":[126],"finally":[128],"conducts":[129],"numerical":[130],"simulations":[131],"real-data":[134],"experiment.":[135],"Experimental":[136],"results":[137],"demonstrate":[138],"our":[140],"significantly":[142],"improves":[143],"robustness":[145],"compared":[146],"existing":[148],"methods,":[149],"even":[150],"outlier-contaminated":[152],"scenarios.":[153]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}