{"id":"https://openalex.org/W2802926706","doi":"https://doi.org/10.1080/00207160.2018.1469748","title":"Error analysis of the moving least-squares method with non-identical sampling","display_name":"Error analysis of the moving least-squares method with non-identical sampling","publication_year":2018,"publication_date":"2018-04-25","ids":{"openalex":"https://openalex.org/W2802926706","doi":"https://doi.org/10.1080/00207160.2018.1469748","mag":"2802926706"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2018.1469748","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2018.1469748","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5080704476","display_name":"Qin Guo","orcid":"https://orcid.org/0000-0002-5355-5857"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qin Guo","raw_affiliation_strings":["School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China"],"raw_orcid":"https://orcid.org/0000-0002-5355-5857","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010523186","display_name":"Peixin Ye","orcid":"https://orcid.org/0000-0002-4706-3223"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Peixin Ye","raw_affiliation_strings":["School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010523186"],"corresponding_institution_ids":["https://openalex.org/I205237279"],"apc_list":null,"apc_paid":null,"fwci":0.4373,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.56260974,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"96","issue":"4","first_page":"767","last_page":"781"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9717000126838684,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9717000126838684,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9682999849319458,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9531000256538391,"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":0.8335754871368408},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6577016115188599},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6530670523643494},{"id":"https://openalex.org/keywords/marginal-distribution","display_name":"Marginal distribution","score":0.5532059669494629},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5500326752662659},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.511218786239624},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48424026370048523},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4697183668613434},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.46145471930503845},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44117966294288635},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20304164290428162},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.14767131209373474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10451918840408325}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8335754871368408},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6577016115188599},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6530670523643494},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.5532059669494629},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5500326752662659},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.511218786239624},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48424026370048523},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4697183668613434},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.46145471930503845},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44117966294288635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20304164290428162},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.14767131209373474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10451918840408325},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2018.1469748","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2018.1469748","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G6776182154","display_name":null,"funder_award_id":"11271199, 11671213","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W237643651","https://openalex.org/W597932189","https://openalex.org/W1623557273","https://openalex.org/W1969696041","https://openalex.org/W1970780859","https://openalex.org/W1972935639","https://openalex.org/W2017332415","https://openalex.org/W2021440127","https://openalex.org/W2042138716","https://openalex.org/W2047970813","https://openalex.org/W2078797044","https://openalex.org/W2089367368","https://openalex.org/W2090761569","https://openalex.org/W2092396945","https://openalex.org/W2095375944","https://openalex.org/W2097285182","https://openalex.org/W2109606373","https://openalex.org/W2114710414","https://openalex.org/W2142563104","https://openalex.org/W2147169375","https://openalex.org/W2468357046","https://openalex.org/W2597348797","https://openalex.org/W2802739963","https://openalex.org/W4238717354","https://openalex.org/W4245558064","https://openalex.org/W4299533062"],"related_works":["https://openalex.org/W2112284452","https://openalex.org/W3085798047","https://openalex.org/W2374269412","https://openalex.org/W371123309","https://openalex.org/W2085500676","https://openalex.org/W2186272223","https://openalex.org/W2038693912","https://openalex.org/W2365096715","https://openalex.org/W2012817876","https://openalex.org/W2332119367"],"abstract_inverted_index":{"We":[0],"derive":[1],"the":[2,6,14,17,36,41,45,49,60,68,75,83],"convergence":[3],"rate":[4,84],"of":[5,25,51,62,74],"moving":[7],"least-squares":[8],"learning":[9],"algorithm":[10,76],"for":[11,44],"regression":[12],"under":[13],"assumption":[15],"that":[16,77],"samples":[18],"are":[19],"drawn":[20],"from":[21],"a":[22,63],"non-identical":[23,46],"sequence":[24,50],"probability":[26,42],"measures.":[27],"The":[28],"error":[29,38,72],"analysis":[30],"is":[31],"carried":[32],"out":[33],"by":[34],"analysing":[35],"drift":[37],"and":[39],"using":[40],"inequalities":[43],"sampling.":[47],"When":[48],"marginal":[52,57],"distributions":[53],"converges":[54],"exponentially":[55],"to":[56,82],"distribution":[58],"in":[59],"dual":[61],"H\u00f6lder":[64],"space,":[65],"we":[66],"obtain":[67],"satisfactory":[69],"capacity":[70],"dependent":[71],"bounds":[73],"can":[78],"be":[79],"arbitrarily":[80],"close":[81],"O(m\u22121).":[85]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
