{"id":"https://openalex.org/W3003878573","doi":"https://doi.org/10.1109/access.2020.2970506","title":"Checking Heteroscedasticity in Partially Linear Single-Index Models Using Pairwise Distance","display_name":"Checking Heteroscedasticity in Partially Linear Single-Index Models Using Pairwise Distance","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3003878573","doi":"https://doi.org/10.1109/access.2020.2970506","mag":"3003878573"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.2970506","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2970506","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08976093.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08976093.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101584695","display_name":"Jian-Qiang Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I124841900","display_name":"Xuzhou University of Technology","ror":"https://ror.org/02315by94","country_code":"CN","type":"education","lineage":["https://openalex.org/I124841900"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian-Qiang Zhao","raw_affiliation_strings":["School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-3846-9739","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, China","institution_ids":["https://openalex.org/I124841900"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101457914","display_name":"Jianquan Li","orcid":"https://orcid.org/0000-0001-8165-904X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jianquan Li","raw_affiliation_strings":["Beijing Ultrapower Software Company Ltd., Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-8165-904X","affiliations":[{"raw_affiliation_string":"Beijing Ultrapower Software Company Ltd., Beijing, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101688889","display_name":"Yan\u2010Yong Zhao","orcid":"https://orcid.org/0000-0003-2354-8469"},"institutions":[{"id":"https://openalex.org/I206777745","display_name":"Nanjing Audit University","ror":"https://ror.org/04zj2bd87","country_code":"CN","type":"education","lineage":["https://openalex.org/I206777745"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan-Yong Zhao","raw_affiliation_strings":["Department of Statistics, Nanjing Audit University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-2354-8469","affiliations":[{"raw_affiliation_string":"Department of Statistics, Nanjing Audit University, Nanjing, China","institution_ids":["https://openalex.org/I206777745"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101584694","display_name":"Junyan He","orcid":"https://orcid.org/0000-0003-3754-8873"},"institutions":[{"id":"https://openalex.org/I124841900","display_name":"Xuzhou University of Technology","ror":"https://ror.org/02315by94","country_code":"CN","type":"education","lineage":["https://openalex.org/I124841900"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junyan He","raw_affiliation_strings":["School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-3754-8873","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, China","institution_ids":["https://openalex.org/I124841900"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023408175","display_name":"Waled Khaled","orcid":"https://orcid.org/0000-0002-7382-7186"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Waled Khaled","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-7382-7186","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1750,"currency":"USD","value_usd":1750},"apc_paid":{"value":1750,"currency":"USD","value_usd":1750},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02448023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":null,"first_page":"25286","last_page":"25298"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9962999820709229,"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":0.9962999820709229,"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":0.9937000274658203,"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/T11911","display_name":"Spatial and Panel Data Analysis","score":0.9897000193595886,"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":0.7682411670684814},{"id":"https://openalex.org/keywords/test-statistic","display_name":"Test statistic","score":0.675401508808136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6547731161117554},{"id":"https://openalex.org/keywords/null-distribution","display_name":"Null distribution","score":0.5264587998390198},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.46933239698410034},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.4637629985809326},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4479314386844635},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.42036372423171997},{"id":"https://openalex.org/keywords/statistic","display_name":"Statistic","score":0.4164230227470398},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.40525543689727783},{"id":"https://openalex.org/keywords/statistical-hypothesis-testing","display_name":"Statistical hypothesis testing","score":0.3403956890106201},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.12146848440170288}],"concepts":[{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.7682411670684814},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.675401508808136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6547731161117554},{"id":"https://openalex.org/C120639","wikidata":"https://www.wikidata.org/wiki/Q7068958","display_name":"Null distribution","level":4,"score":0.5264587998390198},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.46933239698410034},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4637629985809326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4479314386844635},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.42036372423171997},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.4164230227470398},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.40525543689727783},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.3403956890106201},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.12146848440170288}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2020.2970506","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2970506","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08976093.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:14f1cb124a3f479a9a59c9153b69a9fb","is_oa":true,"landing_page_url":"https://doaj.org/article/14f1cb124a3f479a9a59c9153b69a9fb","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":"IEEE Access, Vol 8, Pp 25286-25298 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.2970506","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2970506","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08976093.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1002857706","display_name":null,"funder_award_id":"BK20171073","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2430194705","display_name":null,"funder_award_id":"17KJB110006","funder_id":"https://openalex.org/F4320335440","funder_display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China"},{"id":"https://openalex.org/G3386291493","display_name":null,"funder_award_id":"11701286","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4573771758","display_name":"\u9ad8\u9891\u91d1\u878d\u6570\u636e\u4e0b\u5373\u65f6\u6ce2\u52a8\u7387\u7684\u975e\u53c2\u6570\u4f30\u8ba1\u53ca\u5176\u5e94\u7528\u7814\u7a76","funder_award_id":"11961038","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G570965738","display_name":null,"funder_award_id":"17KJB110006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8841359716","display_name":null,"funder_award_id":"BK20171073","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335440","display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3003878573.pdf","grobid_xml":"https://content.openalex.org/works/W3003878573.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W22760052","https://openalex.org/W135795571","https://openalex.org/W1966548789","https://openalex.org/W1967289386","https://openalex.org/W1978189606","https://openalex.org/W1998808865","https://openalex.org/W2001125876","https://openalex.org/W2005890854","https://openalex.org/W2016868879","https://openalex.org/W2023888753","https://openalex.org/W2031245232","https://openalex.org/W2053020350","https://openalex.org/W2069768629","https://openalex.org/W2080461688","https://openalex.org/W2086067392","https://openalex.org/W2093738981","https://openalex.org/W2128522844","https://openalex.org/W2131195275","https://openalex.org/W2132609392","https://openalex.org/W2136175429","https://openalex.org/W2136454465","https://openalex.org/W2161917006","https://openalex.org/W2189312858","https://openalex.org/W2275719586","https://openalex.org/W2337274292","https://openalex.org/W2610129649","https://openalex.org/W2759516619","https://openalex.org/W2916260300","https://openalex.org/W3000332379","https://openalex.org/W3036417878","https://openalex.org/W4299798163","https://openalex.org/W6779749190"],"related_works":["https://openalex.org/W2088177408","https://openalex.org/W4388584729","https://openalex.org/W2758076833","https://openalex.org/W3136093685","https://openalex.org/W3000603176","https://openalex.org/W2018490949","https://openalex.org/W2568361756","https://openalex.org/W4287817427","https://openalex.org/W2185462963","https://openalex.org/W2978172590"],"abstract_inverted_index":{"In":[0,122],"this":[1,96,107],"article,":[2],"a":[3,32,58,154],"new":[4],"test":[5,24,108],"is":[6,83,110],"proposed":[7,80],"for":[8],"partially":[9],"linear":[10],"single-index":[11],"models":[12],"(PLSIM)":[13],"based":[14],"on":[15,132],"the":[16,20,41,65,68,73,79,87,91,127,133,136,141,144,150],"pairwise":[17],"distances":[18],"of":[19,67,90,106,126,135,143],"sample":[21],"points,":[22],"to":[23,39,62,86,112],"heteroscedasticity.":[25],"The":[26,103],"statistic":[27,34,97,128],"can":[28],"be":[29],"formulated":[30],"as":[31,50],"U":[33],"and":[35,114,153],"does":[36,129],"not":[37,130],"have":[38],"estimate":[40],"conditional":[42],"variance":[43],"function":[44],"by":[45],"using":[46],"nonparametric":[47],"methods,":[48],"such":[49],"kernel,":[51],"local":[52],"polynomial,":[53],"or":[54],"spline.":[55],"We":[56,76],"derive":[57],"computationally":[59],"feasible":[60],"approximation":[61,85],"deal":[63],"with":[64],"complexity":[66],"limit":[69],"zero":[70],"distribution":[71,89],"under":[72],"null":[74,88],"hypothesis.":[75],"prove":[77],"that":[78,95],"bootstrap":[81],"procedure":[82],"valid":[84],"test.":[92],"It":[93],"shows":[94],"has":[98,115],"an":[99],"asymptotically":[100],"normal":[101],"distribution.":[102],"algorithmic":[104],"program":[105],"method":[109],"easy":[111],"implement":[113],"faster":[116],"convergence":[117,124],"than":[118],"some":[119],"existing":[120],"methods.":[121],"addition,":[123],"rate":[125],"depend":[131],"dimensions":[134],"covariates,":[137],"which":[138],"greatly":[139],"reduces":[140],"impact":[142],"dimensional":[145],"curse.":[146],"Finally,":[147],"we":[148],"give":[149],"numerical":[151],"simulations":[152],"real":[155],"data":[156],"example.":[157]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}