{"id":"https://openalex.org/W2764189611","doi":"https://doi.org/10.1080/03610918.2017.1381741","title":"Uniformly strong consistency and Berry-Esseen bound of frequency polygons for <i>\u03b1</i>-mixing samples","display_name":"Uniformly strong consistency and Berry-Esseen bound of frequency polygons for <i>\u03b1</i>-mixing samples","publication_year":2017,"publication_date":"2017-10-04","ids":{"openalex":"https://openalex.org/W2764189611","doi":"https://doi.org/10.1080/03610918.2017.1381741","mag":"2764189611"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2017.1381741","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2017.1381741","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/A5015714617","display_name":"Guodong Xing","orcid":null},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]},{"id":"https://openalex.org/I41317344","display_name":"Jiangxi Science and Technology Normal University","ror":"https://ror.org/04r1zkp10","country_code":"CN","type":"education","lineage":["https://openalex.org/I41317344"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guo-Dong Xing","raw_affiliation_strings":["School of Mathematical Sciences, Xiamen University, Xiamen, China","School of Mathematics & Computer Science, Guangxi Science & Technology Normal University, Laibin, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Xiamen University, Xiamen, China","institution_ids":["https://openalex.org/I191208505"]},{"raw_affiliation_string":"School of Mathematics & Computer Science, Guangxi Science & Technology Normal University, Laibin, China","institution_ids":["https://openalex.org/I41317344"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101512406","display_name":"Shanchao Yang","orcid":"https://orcid.org/0000-0002-4017-3542"},"institutions":[{"id":"https://openalex.org/I29739308","display_name":"Guangxi Normal University","ror":"https://ror.org/02frt9q65","country_code":"CN","type":"education","lineage":["https://openalex.org/I29739308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shan-Chao Yang","raw_affiliation_strings":["School of Mathematics and Statistics, Guangxi Normal University, Guilin, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guangxi Normal University, Guilin, China","institution_ids":["https://openalex.org/I29739308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100631865","display_name":"Xiaohu Li","orcid":"https://orcid.org/0000-0001-8278-3878"},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaohu Li","raw_affiliation_strings":["Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ, USA","institution_ids":["https://openalex.org/I108468826"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015714617"],"corresponding_institution_ids":["https://openalex.org/I191208505","https://openalex.org/I41317344"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.14264018,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"48","issue":"2","first_page":"416","last_page":"430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9973999857902527,"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":0.9973999857902527,"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":0.9959999918937683,"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"}},{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9894999861717224,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7402398586273193},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7237405776977539},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.6865714192390442},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.6797853708267212},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.5727300047874451},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"Uniform convergence","score":0.5284298062324524},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4782649278640747},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4356299936771393},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.43330830335617065},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41748321056365967},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41200560331344604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40049678087234497},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38429415225982666},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37234941124916077},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.33408623933792114},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2093765139579773},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15256422758102417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0749916136264801},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06629949808120728}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7402398586273193},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7237405776977539},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.6865714192390442},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.6797853708267212},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.5727300047874451},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.5284298062324524},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4782649278640747},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4356299936771393},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.43330830335617065},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41748321056365967},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41200560331344604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40049678087234497},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38429415225982666},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37234941124916077},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.33408623933792114},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2093765139579773},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15256422758102417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0749916136264801},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06629949808120728},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610918.2017.1381741","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2017.1381741","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.550000011920929}],"awards":[],"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":18,"referenced_works":["https://openalex.org/W1967985375","https://openalex.org/W1970373309","https://openalex.org/W1976512640","https://openalex.org/W1986727936","https://openalex.org/W1989089774","https://openalex.org/W1992544438","https://openalex.org/W1994895555","https://openalex.org/W2000203647","https://openalex.org/W2031377921","https://openalex.org/W2046412645","https://openalex.org/W2050858914","https://openalex.org/W2056075622","https://openalex.org/W2056871913","https://openalex.org/W2060705818","https://openalex.org/W2079763497","https://openalex.org/W2137157280","https://openalex.org/W2146282816","https://openalex.org/W2360711113"],"related_works":["https://openalex.org/W4380153838","https://openalex.org/W2383204375","https://openalex.org/W2107908243","https://openalex.org/W2001164387","https://openalex.org/W4285786600","https://openalex.org/W4281774867","https://openalex.org/W2972622627","https://openalex.org/W3082176452","https://openalex.org/W2045082303","https://openalex.org/W2891408003"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"the":[3,27,35,41,50,54,65],"frequency":[4],"polygon":[5],"investigated":[6],"by":[7,45],"Scott":[8],"is":[9,58,61],"studied":[10],"as":[11],"a":[12],"nonparametric":[13],"estimator":[14],"for":[15],"\u03b1-mixing":[16],"samples.":[17],"By":[18],"some":[19],"known":[20],"exponent":[21],"and":[22,31],"moment":[23],"inequalities,":[24],"we":[25],"obtain":[26],"uniformly":[28,55],"strong":[29],"consistency":[30],"Berry-Esseen":[32],"bound":[33],"of":[34,53],"estimator.":[36],"The":[37],"present":[38],"results":[39],"relax":[40],"relevant":[42],"conditions":[43],"used":[44],"Carbon":[46],"et":[47],"al.":[48],"Furthermore,":[49],"convergence":[51],"rate":[52],"asymptotic":[56],"normality":[57],"derived,":[59],"which":[60],"O(n\u2212":[62],"1/11)":[63],"under":[64],"given":[66],"conditions.":[67]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-10-20T00:00:00"}
