{"id":"https://openalex.org/W4389994760","doi":"https://doi.org/10.3390/axioms13010004","title":"Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model","display_name":"Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model","publication_year":2023,"publication_date":"2023-12-20","ids":{"openalex":"https://openalex.org/W4389994760","doi":"https://doi.org/10.3390/axioms13010004"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13010004","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010004","pdf_url":"https://www.mdpi.com/2075-1680/13/1/4/pdf?version=1703073430","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/2075-1680/13/1/4/pdf?version=1703073430","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038171448","display_name":"Shida Ma","orcid":"https://orcid.org/0009-0008-9807-0301"},"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":"Shida Ma","raw_affiliation_strings":["College of Science, China University of Petroleum, Qingdao 266580, China"],"raw_orcid":"https://orcid.org/0009-0008-9807-0301","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":"https://openalex.org/A5100567308","display_name":"Yiming Hou","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":"Yiming Hou","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":"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":false,"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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069010339","display_name":"Feng Zhou","orcid":"https://orcid.org/0000-0003-1897-5677"},"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":"Feng Zhou","raw_affiliation_strings":["College of Science, China University of Petroleum, Qingdao 266580, China"],"raw_orcid":"https://orcid.org/0000-0003-1897-5677","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":4,"corresponding_author_ids":["https://openalex.org/A5069010339"],"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":1.1038,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.89193732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"13","issue":"1","first_page":"4","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10841","display_name":"Economic and Environmental Valuation","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9801999926567078,"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/robustness","display_name":"Robustness (evolution)","score":0.6230252981185913},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.6110835075378418},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5558943748474121},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5351783633232117},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.49127358198165894},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.47836536169052124},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4614708423614502},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43503618240356445},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4300243854522705},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20558932423591614}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6230252981185913},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.6110835075378418},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5558943748474121},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5351783633232117},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.49127358198165894},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.47836536169052124},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4614708423614502},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43503618240356445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4300243854522705},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20558932423591614},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13010004","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010004","pdf_url":"https://www.mdpi.com/2075-1680/13/1/4/pdf?version=1703073430","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:0956ea67dc274e61a16e54014578b2d0","is_oa":true,"landing_page_url":"https://doaj.org/article/0956ea67dc274e61a16e54014578b2d0","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 13, Iss 1, p 4 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13010004","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13010004","pdf_url":"https://www.mdpi.com/2075-1680/13/1/4/pdf?version=1703073430","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":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.7400000095367432}],"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"},{"id":"https://openalex.org/G7895523656","display_name":null,"funder_award_id":"2021YFA1000102","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389994760.pdf"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1996742192","https://openalex.org/W2020925091","https://openalex.org/W2022796289","https://openalex.org/W2028226037","https://openalex.org/W2029469881","https://openalex.org/W2030597423","https://openalex.org/W2069627663","https://openalex.org/W2074682976","https://openalex.org/W2100556411","https://openalex.org/W2135046866","https://openalex.org/W2147534083","https://openalex.org/W2166765763","https://openalex.org/W2505756961","https://openalex.org/W2954483373","https://openalex.org/W3089507321","https://openalex.org/W3099697354","https://openalex.org/W4313597626","https://openalex.org/W6765206195","https://openalex.org/W6823589455"],"related_works":["https://openalex.org/W2117229703","https://openalex.org/W3120756218","https://openalex.org/W4256576576","https://openalex.org/W2139276415","https://openalex.org/W2187599770","https://openalex.org/W1975417825","https://openalex.org/W2561368111","https://openalex.org/W2066604793","https://openalex.org/W2913638668","https://openalex.org/W2951054300"],"abstract_inverted_index":{"With":[0],"the":[1,15,19,37,40,58,64,89,94,102,118,146,151,160,163],"widespread":[2],"application":[3],"of":[4,21,34,39,69,96,121],"spatial":[5,22,41,119,152],"data":[6],"in":[7,105,129,133,145],"fields":[8],"like":[9],"econometrics":[10],"and":[11,26,57,66,100,149],"geographic":[12],"information":[13],"science,":[14],"methods":[16],"to":[17,63,126,162],"enhance":[18],"robustness":[20,139],"econometric":[23],"model":[24,43,161],"estimation":[25],"variable":[27,49],"selection":[28,50],"have":[29],"become":[30],"a":[31,48,83],"central":[32],"focus":[33],"research.":[35],"In":[36],"context":[38],"error":[42,122],"(SEM),":[44],"this":[45,70],"paper":[46],"introduces":[47],"method":[51,137],"based":[52],"on":[53],"exponential":[54,90],"square":[55,91],"loss":[56],"adaptive":[59],"lasso":[60],"penalty.":[61],"Due":[62],"non-convex":[65],"non-differentiable":[67],"nature":[68],"proposed":[71,136],"method,":[72],"convex":[73,98],"programming":[74],"is":[75,143,155],"not":[76],"applicable":[77],"for":[78,110],"its":[79],"solution.":[80],"We":[81],"develop":[82],"block":[84],"coordinate":[85],"descent":[86],"algorithm,":[87],"decompose":[88],"component":[92],"into":[93],"difference":[95],"two":[97],"functions,":[99],"utilize":[101],"CCCP":[103],"algorithm":[104],"combination":[106],"with":[107],"parabolic":[108],"interpolation":[109],"optimizing":[111],"problem-solving.":[112],"Numerical":[113],"simulations":[114],"demonstrate":[115],"that":[116],"neglecting":[117],"effects":[120],"terms":[123],"can":[124],"lead":[125],"reduced":[127],"accuracy":[128],"selecting":[130],"zero":[131],"coefficients":[132],"SEM.":[134],"The":[135],"demonstrates":[138],"even":[140],"when":[141,150],"noise":[142],"present":[144],"observed":[147],"values":[148],"weights":[153],"matrix":[154],"inaccurate.":[156],"Finally,":[157],"we":[158],"apply":[159],"Boston":[164],"housing":[165],"dataset.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}