{"id":"https://openalex.org/W4308471298","doi":"https://doi.org/10.1080/03610918.2022.2142241","title":"Limit behaviors of regression function estimator with martingale difference errors","display_name":"Limit behaviors of regression function estimator with martingale difference errors","publication_year":2022,"publication_date":"2022-11-07","ids":{"openalex":"https://openalex.org/W4308471298","doi":"https://doi.org/10.1080/03610918.2022.2142241"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2022.2142241","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2022.2142241","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100353172","display_name":"Chang Liu","orcid":"https://orcid.org/0000-0001-8033-9546"},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chang Liu","raw_affiliation_strings":["College of Mathematics and Information Science, Henan Normal University, Xinxiang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Henan Normal University, Xinxiang, China","institution_ids":["https://openalex.org/I75955062"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028555411","display_name":"Zhen Li","orcid":"https://orcid.org/0000-0002-6743-4829"},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen Li","raw_affiliation_strings":["College of Mathematics and Information Science, Henan Normal University, Xinxiang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Henan Normal University, Xinxiang, China","institution_ids":["https://openalex.org/I75955062"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088213081","display_name":"Yu Miao","orcid":"https://orcid.org/0000-0002-8080-7431"},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu Miao","raw_affiliation_strings":["College of Mathematics and Information Science, Henan Normal University, Xinxiang, China","Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Xinxiang, China"],"raw_orcid":"https://orcid.org/0000-0002-8080-7431","affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Henan Normal University, Xinxiang, China","institution_ids":["https://openalex.org/I75955062"]},{"raw_affiliation_string":"Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Xinxiang, China","institution_ids":["https://openalex.org/I75955062"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088213081"],"corresponding_institution_ids":["https://openalex.org/I75955062"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.16299516,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"53","issue":"9","first_page":"4233","last_page":"4247"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9972000122070312,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8029597997665405},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7829554080963135},{"id":"https://openalex.org/keywords/martingale-difference-sequence","display_name":"Martingale difference sequence","score":0.7035072445869446},{"id":"https://openalex.org/keywords/regression-function","display_name":"Regression function","score":0.6607666611671448},{"id":"https://openalex.org/keywords/martingale","display_name":"Martingale (probability theory)","score":0.6595497131347656},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.623565137386322},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5915927886962891},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5273640751838684},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.49656540155410767},{"id":"https://openalex.org/keywords/strong-consistency","display_name":"Strong consistency","score":0.48338714241981506},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.4546045660972595},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.43581101298332214},{"id":"https://openalex.org/keywords/consistent-estimator","display_name":"Consistent estimator","score":0.4236086905002594},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3590461015701294},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.2076132595539093},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13614311814308167},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05815565586090088}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8029597997665405},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7829554080963135},{"id":"https://openalex.org/C30268764","wikidata":"https://www.wikidata.org/wiki/Q3707378","display_name":"Martingale difference sequence","level":3,"score":0.7035072445869446},{"id":"https://openalex.org/C2988035592","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression function","level":3,"score":0.6607666611671448},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.6595497131347656},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.623565137386322},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5915927886962891},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5273640751838684},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.49656540155410767},{"id":"https://openalex.org/C31388003","wikidata":"https://www.wikidata.org/wiki/Q7624548","display_name":"Strong consistency","level":3,"score":0.48338714241981506},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.4546045660972595},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.43581101298332214},{"id":"https://openalex.org/C164172150","wikidata":"https://www.wikidata.org/wiki/Q1782585","display_name":"Consistent estimator","level":4,"score":0.4236086905002594},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3590461015701294},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.2076132595539093},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13614311814308167},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05815565586090088},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610918.2022.2142241","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2022.2142241","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.550000011920929,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G3309341234","display_name":null,"funder_award_id":"NSFC-11971154","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W418042739","https://openalex.org/W1966037610","https://openalex.org/W1973650304","https://openalex.org/W2006261784","https://openalex.org/W2030086112","https://openalex.org/W2031376680","https://openalex.org/W2038714236","https://openalex.org/W2043847415","https://openalex.org/W2045658596","https://openalex.org/W2048552588","https://openalex.org/W2053672153","https://openalex.org/W2060165663","https://openalex.org/W2062131848","https://openalex.org/W2076576508","https://openalex.org/W2096850081","https://openalex.org/W2112807623","https://openalex.org/W2118020555","https://openalex.org/W2172525224","https://openalex.org/W2348687934","https://openalex.org/W2538467889","https://openalex.org/W2560458561","https://openalex.org/W2887845086","https://openalex.org/W2954652211","https://openalex.org/W3087710273","https://openalex.org/W3201347639"],"related_works":["https://openalex.org/W2114886953","https://openalex.org/W2321373232","https://openalex.org/W2076095938","https://openalex.org/W2061726243","https://openalex.org/W1979459108","https://openalex.org/W2056761152","https://openalex.org/W2044339085","https://openalex.org/W2385492916","https://openalex.org/W2388399940","https://openalex.org/W2156357722"],"abstract_inverted_index":{"In":[0],"the":[1,6,14,22,30,44,52],"present":[2],"paper,":[3],"we":[4],"consider":[5],"nonparametric":[7],"regression":[8],"model":[9],"Yi=g(xi)+\u03b5i,":[10],"1\u2264i\u2264n,":[11],"and":[12,17,26,38,47],"study":[13],"strong":[15,19],"consistency":[16,20],"uniform":[18,48],"of":[21,24,51],"estimator":[23,53],"Priestley":[25],"Chao":[27],"based":[28],"on":[29],"martingale":[31],"difference":[32],"errors.":[33],"These":[34],"results":[35],"partially":[36],"extend":[37],"improve":[39],"some":[40],"known":[41],"works.":[42],"Furthermore,":[43],"moment":[45,49],"convergency":[46,50],"are":[54],"established":[55],"also.":[56]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-01-08T20:05:33.558190","created_date":"2025-10-10T00:00:00"}
