{"id":"https://openalex.org/W2794174186","doi":"https://doi.org/10.1080/03610918.2019.1655575","title":"Non-parametric estimation of the first-order Sobol indices with bootstrap bandwidth","display_name":"Non-parametric estimation of the first-order Sobol indices with bootstrap bandwidth","publication_year":2019,"publication_date":"2019-08-23","ids":{"openalex":"https://openalex.org/W2794174186","doi":"https://doi.org/10.1080/03610918.2019.1655575","mag":"2794174186"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2019.1655575","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1655575","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1803.03333","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067850502","display_name":"Maikol Sol\u00eds","orcid":"https://orcid.org/0000-0002-8776-6142"},"institutions":[{"id":"https://openalex.org/I31944674","display_name":"Universidad de Costa Rica","ror":"https://ror.org/02yzgww51","country_code":"CR","type":"education","lineage":["https://openalex.org/I31944674"]}],"countries":["CR"],"is_corresponding":true,"raw_author_name":"Maikol Sol\u00eds","raw_affiliation_strings":["Centro de Investigaci\u00f3n en Matem\u00e1tica Pura y Aplicada, Escuela de Matem\u00e1tica, Universidad de Costa Rica, San Pedro, Costa Rica","University of Costa Rica,"],"raw_orcid":"https://orcid.org/0000-0002-8776-6142","affiliations":[{"raw_affiliation_string":"Centro de Investigaci\u00f3n en Matem\u00e1tica Pura y Aplicada, Escuela de Matem\u00e1tica, Universidad de Costa Rica, San Pedro, Costa Rica","institution_ids":["https://openalex.org/I31944674"]},{"raw_affiliation_string":"University of Costa Rica,","institution_ids":["https://openalex.org/I31944674"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067850502"],"corresponding_institution_ids":["https://openalex.org/I31944674"],"apc_list":null,"apc_paid":null,"fwci":0.1432,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52319498,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"50","issue":"9","first_page":"2497","last_page":"2512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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":0.9753000140190125,"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/T10396","display_name":"Fatigue and fracture mechanics","score":0.9663000106811523,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sobol-sequence","display_name":"Sobol sequence","score":0.8366823196411133},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6784873604774475},{"id":"https://openalex.org/keywords/nonparametric-regression","display_name":"Nonparametric regression","score":0.6049050092697144},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.5987615585327148},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.5789738893508911},{"id":"https://openalex.org/keywords/kernel-smoother","display_name":"Kernel smoother","score":0.5668768882751465},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5018675327301025},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.46048009395599365},{"id":"https://openalex.org/keywords/kernel-regression","display_name":"Kernel regression","score":0.4568946361541748},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43917250633239746},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4236992597579956},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4198407530784607},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.362521231174469},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.3067800998687744},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22309905290603638},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.2060401439666748},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1914740800857544},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07690349221229553}],"concepts":[{"id":"https://openalex.org/C49740808","wikidata":"https://www.wikidata.org/wiki/Q7550116","display_name":"Sobol sequence","level":3,"score":0.8366823196411133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6784873604774475},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.6049050092697144},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.5987615585327148},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.5789738893508911},{"id":"https://openalex.org/C27406209","wikidata":"https://www.wikidata.org/wiki/Q6394203","display_name":"Kernel smoother","level":5,"score":0.5668768882751465},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5018675327301025},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.46048009395599365},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.4568946361541748},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43917250633239746},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4236992597579956},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4198407530784607},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.362521231174469},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3067800998687744},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22309905290603638},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.2060401439666748},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1914740800857544},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07690349221229553},{"id":"https://openalex.org/C75866337","wikidata":"https://www.wikidata.org/wiki/Q7280263","display_name":"Radial basis function kernel","level":4,"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/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/03610918.2019.1655575","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1655575","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"},{"id":"pmh:oai:arXiv.org:1803.03333","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.03333","pdf_url":"https://arxiv.org/pdf/1803.03333","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2794174186","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.03333.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1803.03333","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.03333","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1803.03333","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.03333","pdf_url":"https://arxiv.org/pdf/1803.03333","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1871638094","display_name":null,"funder_award_id":"821\u2013B4\u2013257","funder_id":"https://openalex.org/F4320335005","funder_display_name":"Vicerrector\u00eda de Investigaci\u00f3n, Universidad de Costa Rica"}],"funders":[{"id":"https://openalex.org/F4320323217","display_name":"Universidad de Costa Rica","ror":"https://ror.org/02yzgww51"},{"id":"https://openalex.org/F4320335005","display_name":"Vicerrector\u00eda de Investigaci\u00f3n, Universidad de Costa Rica","ror":"https://ror.org/02yzgww51"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2794174186.pdf","grobid_xml":"https://content.openalex.org/works/W2794174186.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W100464641","https://openalex.org/W163102935","https://openalex.org/W638544165","https://openalex.org/W1511694993","https://openalex.org/W1542323827","https://openalex.org/W1887263824","https://openalex.org/W1911106672","https://openalex.org/W1973492181","https://openalex.org/W1973546808","https://openalex.org/W1980609382","https://openalex.org/W1993294688","https://openalex.org/W1994249905","https://openalex.org/W1998515634","https://openalex.org/W2000836282","https://openalex.org/W2006037565","https://openalex.org/W2010006919","https://openalex.org/W2029767409","https://openalex.org/W2034562813","https://openalex.org/W2042661604","https://openalex.org/W2044771513","https://openalex.org/W2045609516","https://openalex.org/W2050341914","https://openalex.org/W2060003311","https://openalex.org/W2065057616","https://openalex.org/W2074931146","https://openalex.org/W2084643575","https://openalex.org/W2091982351","https://openalex.org/W2093701508","https://openalex.org/W2097441841","https://openalex.org/W2101589741","https://openalex.org/W2102129645","https://openalex.org/W2103908342","https://openalex.org/W2110785335","https://openalex.org/W2151868609","https://openalex.org/W2252331380","https://openalex.org/W2464608731","https://openalex.org/W2582743722","https://openalex.org/W2963034918","https://openalex.org/W2995161752"],"related_works":["https://openalex.org/W2949196923","https://openalex.org/W2163121223","https://openalex.org/W2950162663","https://openalex.org/W2018677501","https://openalex.org/W2028075016","https://openalex.org/W2508410793","https://openalex.org/W2094180958","https://openalex.org/W1483401836","https://openalex.org/W2002711615","https://openalex.org/W2312680600","https://openalex.org/W2915798644","https://openalex.org/W2765785497","https://openalex.org/W2899923608","https://openalex.org/W2395341615","https://openalex.org/W2749008056","https://openalex.org/W2731953661","https://openalex.org/W2743176246","https://openalex.org/W3114547982","https://openalex.org/W3157820090","https://openalex.org/W2910780827"],"abstract_inverted_index":{"Suppose":[0],"that":[1],"Y=\u03c8(X1,\u2026,Xp),":[2],"where":[3],"(X1,\u2026,Xp)\u22a4":[4],"are":[5],"random":[6],"inputs,":[7],"Y":[8,29],"is":[9,14,67,85],"the":[10,23,32,54,59,62,77,82,107,112,117,122,125,128,133],"output,":[11],"and":[12,64,110],"\u03c8(\u00b7)":[13],"an":[15],"unknown":[16],"link":[17,60],"function.":[18],"The":[19,49,69],"Sobol":[20,129],"indices":[21,57],"gauge":[22],"sensitivity":[24],"of":[25,120],"each":[26],"X":[27],"against":[28],"by":[30],"estimating":[31],"regression":[33,114],"curve\u2019s":[34],"variability":[35],"between":[36,61],"them.":[37],"In":[38],"this":[39,89],"paper,":[40],"we":[41,100,136],"estimate":[42,53],"these":[43],"curves":[44],"with":[45,141],"a":[46,73,94,102],"kernel-based":[47,70],"method.":[48],"method":[50,84],"allows":[51],"to":[52,75,87],"first":[55],"order":[56],"when":[58],"independent":[63],"dependent":[65],"variables":[66],"unknown.":[68],"methods":[71],"need":[72],"bandwidth":[74],"average":[76],"observations.":[78],"For":[79],"finite":[80],"samples,":[81],"cross-validation":[83],"famous":[86],"decide":[88],"bandwidth.":[90],"However,":[91],"it":[92],"produces":[93],"structural":[95],"bias.":[96],"To":[97,131],"remedy":[98],"this,":[99],"propose":[101],"bootstrap":[103],"procedure":[104,123],"which":[105],"reconstruct":[106],"model":[108],"residuals":[109],"re-estimate":[111],"non-parametric":[113],"curve.":[115],"With":[116],"new":[118],"set":[119],"curves,":[121],"corrects":[124],"bias":[126],"in":[127],"index.":[130],"test":[132],"developed":[134],"method,":[135],"implemented":[137],"simulated":[138],"numerical":[139],"examples":[140],"complex":[142],"functions.":[143]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
