{"id":"https://openalex.org/W1998293141","doi":"https://doi.org/10.1214/aos/1176348657","title":"Using Stopping Rules to Bound the Mean Integrated Squared Error in Density Estimation","display_name":"Using Stopping Rules to Bound the Mean Integrated Squared Error in Density Estimation","publication_year":1992,"publication_date":"1992-06-01","ids":{"openalex":"https://openalex.org/W1998293141","doi":"https://doi.org/10.1214/aos/1176348657","mag":"1998293141"},"language":"en","primary_location":{"id":"doi:10.1214/aos/1176348657","doi":"https://doi.org/10.1214/aos/1176348657","is_oa":true,"landing_page_url":"https://doi.org/10.1214/aos/1176348657","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-20/issue-2/Using-Stopping-Rules-to-Bound-the-Mean-Integrated-Squared-Error/10.1214/aos/1176348657.pdf","source":{"id":"https://openalex.org/S119757635","display_name":"The Annals of Statistics","issn_l":"0090-5364","issn":["0090-5364","2168-8966"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Statistics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-20/issue-2/Using-Stopping-Rules-to-Bound-the-Mean-Integrated-Squared-Error/10.1214/aos/1176348657.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075132725","display_name":"Adam T. Martinsek","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Adam T. Martinsek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5075132725"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9175,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.74820816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"2","first_page":"797","last_page":"806"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.8413000106811523,"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":0.8413000106811523,"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/T13500","display_name":"Probability and Statistical Research","score":0.1143999993801117,"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/T13141","display_name":"Statistical Methods and Applications","score":0.010599999688565731,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stopping-criterion","display_name":"stopping rules","score":0.9290000200271606},{"id":"https://openalex.org/keywords/mean-integrated-squared-error","display_name":"mean integrated squared error","score":0.9940000176429749},{"id":"https://openalex.org/keywords/density-estimation","display_name":"density estimation","score":0.902999997138977},{"id":"https://openalex.org/keywords/kernel-density-estimation","display_name":"kernel density estimation","score":0.847000002861023},{"id":"https://openalex.org/keywords/sample-size-calculation","display_name":"sample size determination","score":0.6940000057220459},{"id":"https://openalex.org/keywords/asymptotic-efficiency","display_name":"asymptotic efficiency","score":0.8309999704360962},{"id":"https://openalex.org/keywords/data-driven-bandwidth-selection","display_name":"data-driven bandwidth selection","score":0.8569999933242798},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.36399999260902405}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.902935266494751},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.7103197574615479},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6929845809936523},{"id":"https://openalex.org/C2983961125","wikidata":"https://www.wikidata.org/wiki/Q1288707","display_name":"Stopping rule","level":2,"score":0.5998926162719727},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.5849948525428772},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.5809337496757507},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5649129748344421},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.50547194480896},{"id":"https://openalex.org/C181243257","wikidata":"https://www.wikidata.org/wiki/Q1693522","display_name":"Sample mean and sample covariance","level":3,"score":0.49681809544563293},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4729235768318176},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4383169710636139},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4335973262786865},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4121952950954437},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.37907689809799194},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2613275945186615},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24990692734718323},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22575414180755615},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.09210193157196045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1214/aos/1176348657","doi":"https://doi.org/10.1214/aos/1176348657","is_oa":true,"landing_page_url":"https://doi.org/10.1214/aos/1176348657","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-20/issue-2/Using-Stopping-Rules-to-Bound-the-Mean-Integrated-Squared-Error/10.1214/aos/1176348657.pdf","source":{"id":"https://openalex.org/S119757635","display_name":"The Annals of Statistics","issn_l":"0090-5364","issn":["0090-5364","2168-8966"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Statistics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.aos/1176348657","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.aos/1176348657","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1214/aos/1176348657","doi":"https://doi.org/10.1214/aos/1176348657","is_oa":true,"landing_page_url":"https://doi.org/10.1214/aos/1176348657","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-20/issue-2/Using-Stopping-Rules-to-Bound-the-Mean-Integrated-Squared-Error/10.1214/aos/1176348657.pdf","source":{"id":"https://openalex.org/S119757635","display_name":"The Annals of Statistics","issn_l":"0090-5364","issn":["0090-5364","2168-8966"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1998293141.pdf","grobid_xml":"https://content.openalex.org/works/W1998293141.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1547885621","https://openalex.org/W1973678262","https://openalex.org/W1991164204","https://openalex.org/W2004840619","https://openalex.org/W2010879086","https://openalex.org/W2011175416","https://openalex.org/W2014268383","https://openalex.org/W2014700748","https://openalex.org/W2043277109","https://openalex.org/W2062892638","https://openalex.org/W2067848592","https://openalex.org/W2068659855","https://openalex.org/W2079074506","https://openalex.org/W2094771755","https://openalex.org/W2110829452","https://openalex.org/W2129905273","https://openalex.org/W2162271708","https://openalex.org/W2992131518"],"related_works":["https://openalex.org/W2018171363","https://openalex.org/W2083798384","https://openalex.org/W4235289919","https://openalex.org/W1998293141","https://openalex.org/W4299285657","https://openalex.org/W2056020109","https://openalex.org/W2074593928","https://openalex.org/W2009411941","https://openalex.org/W2963486287","https://openalex.org/W1971018733"],"abstract_inverted_index":{"Suppose":[0,39],"$X_1,X_2,\\ldots,X_n$":[1],"are":[2,130,136],"i.i.d.":[3],"with":[4],"unknown":[5],"density":[6,91],"$f$.":[7],"There":[8],"is":[9,53,94,102,114],"a":[10,25,46,87,99,121],"well-known":[11],"expression":[12,65],"for":[13,66,104,132],"the":[14,34,37,51,63,67,81,90,105,109],"asymptotic":[15,64],"mean":[16],"integrated":[17],"squared":[18],"error":[19],"(MISE)":[20],"in":[21,120],"estimating":[22],"$f$":[23],"by":[24],"kernel":[26,35],"estimate":[27],"$\\hat{f}_n$,":[28],"under":[29],"certain":[30,122],"conditions":[31],"on":[32,62,86],"$f$,":[33],"and":[36,111],"bandwidth.":[38],"that":[40,50,92,135],"one":[41,69],"would":[42],"like":[43],"to":[44,76,116,142],"choose":[45],"sample":[47,74,83],"size":[48,75,84],"so":[49],"MISE":[52],"smaller":[54],"than":[55],"some":[56],"preassigned":[57],"positive":[58],"number":[59],"$w$.":[60],"Based":[61],"MISE,":[68,110],"can":[70],"identify":[71],"an":[72],"appropriate":[73,82],"solve":[77],"this":[78,97,112],"problem.":[79],"However,":[80],"depends":[85],"functional":[88],"of":[89,107],"typically":[93],"unknown.":[95],"In":[96],"paper,":[98],"stopping":[100],"rule":[101,113],"proposed":[103],"purpose":[106],"bounding":[108],"shown":[115],"be":[117],"asymptotically":[118,137],"efficient":[119],"sense":[123],"as":[124,139],"$w$":[125],"approaches":[126],"zero.":[127],"These":[128],"results":[129],"obtained":[131],"data-driven":[133],"bandwidths":[134],"optimal":[138],"$n$":[140],"goes":[141],"infinity.":[143]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2025-10-10T00:00:00"}