{"id":"https://openalex.org/W3111239411","doi":"https://doi.org/10.1080/03610918.2020.1851714","title":"Laws of large numbers and complete convergence for WOD random variables and their applications","display_name":"Laws of large numbers and complete convergence for WOD random variables and their applications","publication_year":2020,"publication_date":"2020-12-08","ids":{"openalex":"https://openalex.org/W3111239411","doi":"https://doi.org/10.1080/03610918.2020.1851714","mag":"3111239411"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2020.1851714","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2020.1851714","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/A5090975668","display_name":"Chi Yao","orcid":null},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chi Yao","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, P.R. China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033126775","display_name":"Yongping He","orcid":null},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongping He","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, P.R. China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111817706","display_name":"Rui Wang","orcid":"https://orcid.org/0009-0008-7124-077X"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Wang","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, P.R. China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100633768","display_name":"Xuejun Wang","orcid":"https://orcid.org/0000-0001-5895-936X"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xuejun Wang","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, P.R. China","institution_ids":["https://openalex.org/I143868143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100633768"],"corresponding_institution_ids":["https://openalex.org/I143868143"],"apc_list":null,"apc_paid":null,"fwci":0.1795,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.5894024,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"52","issue":"1","first_page":"175","last_page":"195"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9998999834060669,"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":0.9998999834060669,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9794999957084656,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthant","display_name":"Orthant","score":0.8592867851257324},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7903919219970703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7512272596359253},{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"Law of large numbers","score":0.6227808594703674},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.5682466626167297},{"id":"https://openalex.org/keywords/proofs-of-convergence-of-random-variables","display_name":"Proofs of convergence of random variables","score":0.5500609874725342},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.48398685455322266},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4810469448566437},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.43205520510673523},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43085089325904846},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.334234356880188},{"id":"https://openalex.org/keywords/sum-of-normally-distributed-random-variables","display_name":"Sum of normally distributed random variables","score":0.10767140984535217},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09652405977249146}],"concepts":[{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.8592867851257324},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7903919219970703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7512272596359253},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.6227808594703674},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.5682466626167297},{"id":"https://openalex.org/C206190082","wikidata":"https://www.wikidata.org/wiki/Q7250031","display_name":"Proofs of convergence of random variables","level":5,"score":0.5500609874725342},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.48398685455322266},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4810469448566437},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.43205520510673523},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43085089325904846},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.334234356880188},{"id":"https://openalex.org/C182514268","wikidata":"https://www.wikidata.org/wiki/Q7636889","display_name":"Sum of normally distributed random variables","level":4,"score":0.10767140984535217},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09652405977249146},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610918.2020.1851714","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2020.1851714","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":[{"id":"https://metadata.un.org/sdg/10","score":0.44999998807907104,"display_name":"Reduced inequalities"},{"id":"https://metadata.un.org/sdg/1","score":0.4000000059604645,"display_name":"No poverty"}],"awards":[{"id":"https://openalex.org/G4542601594","display_name":null,"funder_award_id":"1808085QA03, 1908085QA01, 1908085QA07","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"},{"id":"https://openalex.org/G8762670019","display_name":null,"funder_award_id":"11671012, 11871072, 11701004, 11701005","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"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W840983370","https://openalex.org/W1966695467","https://openalex.org/W1973632040","https://openalex.org/W1973650304","https://openalex.org/W1981604690","https://openalex.org/W1991105238","https://openalex.org/W2006364212","https://openalex.org/W2021457219","https://openalex.org/W2030163309","https://openalex.org/W2038714236","https://openalex.org/W2039528852","https://openalex.org/W2040246726","https://openalex.org/W2040378909","https://openalex.org/W2059507684","https://openalex.org/W2101626133","https://openalex.org/W2126249246","https://openalex.org/W2126299964","https://openalex.org/W2126797434","https://openalex.org/W2156871169","https://openalex.org/W2293797166","https://openalex.org/W2343529823","https://openalex.org/W2497265874","https://openalex.org/W2508109141","https://openalex.org/W2595218193","https://openalex.org/W2618715772","https://openalex.org/W2804296734"],"related_works":["https://openalex.org/W3141002044","https://openalex.org/W2794060858","https://openalex.org/W2482931657","https://openalex.org/W4315628691","https://openalex.org/W4406117673","https://openalex.org/W1995336439","https://openalex.org/W1521061676","https://openalex.org/W3152802855","https://openalex.org/W2907889314","https://openalex.org/W3014367349"],"abstract_inverted_index":{"By":[0],"using":[1],"the":[2,12,21,48,52,74],"Marcinkiewicz-Zygmund":[3],"type":[4,8],"inequality":[5],"and":[6,20,28,51],"Rosenthal":[7],"inequality,":[9],"we":[10,67],"study":[11],"Lr":[13,49],"convergence,":[14],"weak":[15],"law":[16],"of":[17,31,33,47,76],"large":[18],"numbers":[19],"complete":[22,53],"convergence":[23,50,54],"for":[24,39],"usual":[25],"normed":[26],"sums":[27,30],"weighted":[29],"arrays":[32],"rowwise":[34],"widely":[35],"orthant":[36],"dependent":[37],"(WOD,":[38],"short)":[40],"random":[41],"variables.":[42],"In":[43],"addition,":[44],"some":[45],"applications":[46],"to":[55,72],"nonparametric":[56],"regression":[57],"models":[58],"based":[59],"on":[60],"WOD":[61],"errors":[62],"are":[63],"provided.":[64],"At":[65],"last,":[66],"provide":[68],"a":[69],"numerical":[70],"simulation":[71],"verify":[73],"validity":[75],"our":[77],"theoretical":[78],"result.":[79]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}