{"id":"https://openalex.org/W4282583678","doi":"https://doi.org/10.3390/sym14061200","title":"Variable Selection of Heterogeneous Spatial Autoregressive Models via Double-Penalized Likelihood","display_name":"Variable Selection of Heterogeneous Spatial Autoregressive Models via Double-Penalized Likelihood","publication_year":2022,"publication_date":"2022-06-10","ids":{"openalex":"https://openalex.org/W4282583678","doi":"https://doi.org/10.3390/sym14061200"},"language":"en","primary_location":{"id":"doi:10.3390/sym14061200","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14061200","pdf_url":"https://www.mdpi.com/2073-8994/14/6/1200/pdf?version=1654841292","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/2073-8994/14/6/1200/pdf?version=1654841292","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023014297","display_name":"Ruiqin Tian","orcid":"https://orcid.org/0000-0002-9163-1056"},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruiqin Tian","raw_affiliation_strings":["School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China","institution_ids":["https://openalex.org/I163151501"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022722138","display_name":"Miaojie Xia","orcid":"https://orcid.org/0000-0003-1263-3457"},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Miaojie Xia","raw_affiliation_strings":["School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"],"raw_orcid":"https://orcid.org/0000-0003-1263-3457","affiliations":[{"raw_affiliation_string":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China","institution_ids":["https://openalex.org/I163151501"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019795352","display_name":"Dengke Xu","orcid":"https://orcid.org/0000-0002-0903-9601"},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dengke Xu","raw_affiliation_strings":["College of Economics, Hangzhou Dianzi University, Hangzhou 310018, China"],"raw_orcid":"https://orcid.org/0000-0002-0903-9601","affiliations":[{"raw_affiliation_string":"College of Economics, Hangzhou Dianzi University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I50760025"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019795352"],"corresponding_institution_ids":["https://openalex.org/I50760025"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.2136,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65803127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"14","issue":"6","first_page":"1200","last_page":"1200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9904000163078308,"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/T11014","display_name":"Regional Economics and Spatial Analysis","score":0.9894999861717224,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/heteroscedasticity","display_name":"Heteroscedasticity","score":0.7461948394775391},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.6879996061325073},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5657678842544556},{"id":"https://openalex.org/keywords/model-selection","display_name":"Model selection","score":0.5555492043495178},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5543053150177002},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5238093137741089},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.4858505427837372},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.4844968020915985},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4725710451602936},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4657061696052551},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4595377445220947},{"id":"https://openalex.org/keywords/spatial-analysis","display_name":"Spatial analysis","score":0.4451330900192261},{"id":"https://openalex.org/keywords/star-model","display_name":"STAR model","score":0.4235248565673828},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.4230788052082062},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4224488139152527},{"id":"https://openalex.org/keywords/feature-selection","display_name":"Feature selection","score":0.42123955488204956},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.15639621019363403},{"id":"https://openalex.org/keywords/autoregressive-integrated-moving-average","display_name":"Autoregressive integrated moving average","score":0.13660317659378052},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09261703491210938}],"concepts":[{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.7461948394775391},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.6879996061325073},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5657678842544556},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.5555492043495178},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5543053150177002},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5238093137741089},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.4858505427837372},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.4844968020915985},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4725710451602936},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4657061696052551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4595377445220947},{"id":"https://openalex.org/C159620131","wikidata":"https://www.wikidata.org/wiki/Q1938983","display_name":"Spatial analysis","level":2,"score":0.4451330900192261},{"id":"https://openalex.org/C194657046","wikidata":"https://www.wikidata.org/wiki/Q7394685","display_name":"STAR model","level":4,"score":0.4235248565673828},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4230788052082062},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4224488139152527},{"id":"https://openalex.org/C148483581","wikidata":"https://www.wikidata.org/wiki/Q446488","display_name":"Feature selection","level":2,"score":0.42123955488204956},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.15639621019363403},{"id":"https://openalex.org/C24338571","wikidata":"https://www.wikidata.org/wiki/Q2566298","display_name":"Autoregressive integrated moving average","level":3,"score":0.13660317659378052},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09261703491210938},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"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/sym14061200","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14061200","pdf_url":"https://www.mdpi.com/2073-8994/14/6/1200/pdf?version=1654841292","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:4974f3f6b61a4c20a6d737971f79be9b","is_oa":true,"landing_page_url":"https://doaj.org/article/4974f3f6b61a4c20a6d737971f79be9b","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 6, p 1200 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/6/1200/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14061200","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/sym14061200","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14061200","pdf_url":"https://www.mdpi.com/2073-8994/14/6/1200/pdf?version=1654841292","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":[{"score":0.5199999809265137,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4282583678.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1527882638","https://openalex.org/W1978926447","https://openalex.org/W1989765480","https://openalex.org/W1993513030","https://openalex.org/W2007685135","https://openalex.org/W2009854401","https://openalex.org/W2020925091","https://openalex.org/W2028226037","https://openalex.org/W2045901075","https://openalex.org/W2049696899","https://openalex.org/W2071673199","https://openalex.org/W2074682976","https://openalex.org/W2076953851","https://openalex.org/W2086205459","https://openalex.org/W2090343436","https://openalex.org/W2112531842","https://openalex.org/W2135046866","https://openalex.org/W2146326366","https://openalex.org/W2560732761","https://openalex.org/W2587708847","https://openalex.org/W2611086616","https://openalex.org/W2790267535","https://openalex.org/W2800815808","https://openalex.org/W2804868497","https://openalex.org/W2935670873","https://openalex.org/W2964382960","https://openalex.org/W2971796726","https://openalex.org/W3022514790","https://openalex.org/W3091440130","https://openalex.org/W3126676292"],"related_works":["https://openalex.org/W1676609285","https://openalex.org/W3148934225","https://openalex.org/W2351648145","https://openalex.org/W2038165226","https://openalex.org/W2372708426","https://openalex.org/W2371672154","https://openalex.org/W2161877893","https://openalex.org/W200497649","https://openalex.org/W4388491989","https://openalex.org/W2058049563"],"abstract_inverted_index":{"Heteroscedasticity":[0],"is":[1,16,62],"often":[2],"encountered":[3],"in":[4,18,37],"spatial-data":[5],"analysis,":[6],"so":[7],"a":[8,55,89],"new":[9],"class":[10],"of":[11,40,78,93],"heterogeneous":[12],"spatial":[13],"autoregressive":[14],"models":[15],"introduced":[17],"this":[19],"paper,":[20],"where":[21],"the":[22,38,44,49,73,79,94,102],"variance":[23,52],"parameters":[24],"are":[25,35,82,98],"allowed":[26],"to":[27,64,100],"depend":[28],"on":[29],"some":[30],"explanatory":[31],"variables.":[32,68],"Here,":[33],"we":[34],"interested":[36],"problem":[39],"parameter":[41],"estimation":[42],"and":[43,51,75,88],"variable":[45],"selection":[46],"for":[47],"both":[48,85],"mean":[50],"models.":[53],"Then,":[54],"unified":[56],"procedure":[57],"via":[58],"double-penalized":[59],"quasi-maximum":[60],"likelihood":[61],"proposed,":[63],"simultaneously":[65],"select":[66],"important":[67],"Under":[69],"certain":[70],"regular":[71],"conditions,":[72],"consistency":[74],"oracle":[76],"property":[77],"resulting":[80],"estimators":[81],"established.":[83],"Finally,":[84],"simulation":[86],"studies":[87],"real":[90],"data":[91,97],"analysis":[92],"Boston":[95],"housing":[96],"carried":[99],"illustrate":[101],"developed":[103],"methodology.":[104]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
