{"id":"https://openalex.org/W2012004107","doi":"https://doi.org/10.1214/009053607000000271","title":"Spatial aggregation of local likelihood estimates with applications to classification","display_name":"Spatial aggregation of local likelihood estimates with applications to classification","publication_year":2007,"publication_date":"2007-10-01","ids":{"openalex":"https://openalex.org/W2012004107","doi":"https://doi.org/10.1214/009053607000000271","mag":"2012004107"},"language":"en","primary_location":{"id":"doi:10.1214/009053607000000271","doi":"https://doi.org/10.1214/009053607000000271","is_oa":true,"landing_page_url":"https://doi.org/10.1214/009053607000000271","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-35/issue-5/Spatial-aggregation-of-local-likelihood-estimates-with-applications-to-classification/10.1214/009053607000000271.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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-35/issue-5/Spatial-aggregation-of-local-likelihood-estimates-with-applications-to-classification/10.1214/009053607000000271.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023650696","display_name":"Denis Vital'evich Belomestny","orcid":"https://orcid.org/0000-0002-9482-6430","observed_orcids":["https://orcid.org/0000-0002-9482-6430"]},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Denis Belomestny","raw_affiliation_strings":["Weierstrass Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035705885","display_name":"Vladimir Grigor'evich Spokoiny","orcid":"https://orcid.org/0000-0002-2040-3427","observed_orcids":["https://orcid.org/0000-0002-2040-3427"]},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Vladimir Spokoiny","raw_affiliation_strings":["Weierstrass Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute","institution_ids":["https://openalex.org/I4210092021"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":null,"apc_paid":null,"fwci":5.5118,"has_fulltext":true,"cited_by_count":37,"citation_normalized_percentile":{"value":0.96187186,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"35","issue":"5","first_page":"2287","last_page":"2311"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9976000189781189,"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":0.9976000189781189,"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/T11911","display_name":"Spatial and Panel Data Analysis","score":0.0010000000474974513,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"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/T13141","display_name":"Statistical Methods and Applications","score":0.00019999999494757503,"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/spatial-aggregation","display_name":"spatial aggregation","score":0.8889999985694885},{"id":"https://openalex.org/keywords/local-likelihood-estimation","display_name":"local likelihood estimation","score":0.9580000042915344},{"id":"https://openalex.org/keywords/nonparametric-regression","display_name":"nonparametric regression","score":0.7210000157356262},{"id":"https://openalex.org/keywords/oracle-inequalities","display_name":"oracle inequalities","score":0.6610000133514404},{"id":"https://openalex.org/keywords/risk-minimization","display_name":"risk minimization","score":0.5220000147819519},{"id":"https://openalex.org/keywords/parameter-selection","display_name":"parameter selection","score":0.6000000238418579},{"id":"https://openalex.org/keywords/classification","display_name":"classification","score":0.6119999885559082},{"id":"https://openalex.org/keywords/binary-response-models","display_name":"binary response models","score":0.9459999799728394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8174957036972046},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6856282353401184},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.601982057094574},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.5904713869094849},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4752621054649353},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.44611504673957825},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4123803973197937},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3904011845588684},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.37710171937942505},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3678274154663086},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35786202549934387},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35296785831451416},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":11,"locations":[{"id":"doi:10.1214/009053607000000271","doi":"https://doi.org/10.1214/009053607000000271","is_oa":true,"landing_page_url":"https://doi.org/10.1214/009053607000000271","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-35/issue-5/Spatial-aggregation-of-local-likelihood-estimates-with-applications-to-classification/10.1214/009053607000000271.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:arXiv.org:0712.0939","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0712.0939","pdf_url":"https://arxiv.org/pdf/0712.0939","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,"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":null,"raw_type":"text"},{"id":"pmh:oai:RePEc:hum:wpaper:sfb649dp2006-036","doi":null,"is_oa":false,"landing_page_url":"http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-036.pdf","pdf_url":"http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-036.pdf","source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"preprint"},{"id":"pmh:oai:RePEc:zbw:sfb649:sfb649dp2006-036","doi":null,"is_oa":false,"landing_page_url":"https://www.econstor.eu/bitstream/10419/25117/1/512479518.PDF","pdf_url":"https://www.econstor.eu/bitstream/10419/25117/1/512479518.PDF","source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"preprint"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.769.9035","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.769.9035","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0712.0939.pdf","raw_type":"text"},{"id":"mag:3125148838","doi":null,"is_oa":false,"landing_page_url":"https://econpapers.repec.org/RePEc:hum:wpaper:sfb649dp2006-036","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RePEc: Research Papers in Economics","raw_type":null},{"id":"pmh:oai:CULeuclid:euclid.aos/1194461731","doi":null,"is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.aos/1194461731","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"},{"id":"pmh:oai:econstor.eu:10419/25117","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10419/25117","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:workingPaper"},{"id":"pmh:oai:edoc.hu-berlin.de:18452/4618","doi":null,"is_oa":false,"landing_page_url":"https://edoc.hu-berlin.de/18452/4618","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"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":"workingPaper"},{"id":"doi:10.48550/arxiv.0712.0939","doi":"https://doi.org/10.48550/arxiv.0712.0939","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0712.0939","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,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.18452/3966","doi":"https://doi.org/10.18452/3966","is_oa":true,"landing_page_url":"https://doi.org/10.18452/3966","pdf_url":null,"source":{"id":"https://openalex.org/S4306400923","display_name":"edoc Publication server (Humboldt University of Berlin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I39343248","host_organization_name":"Humboldt-Universit\u00e4t zu Berlin","host_organization_lineage":["https://openalex.org/I39343248"],"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":null}],"best_oa_location":{"id":"doi:10.1214/009053607000000271","doi":"https://doi.org/10.1214/009053607000000271","is_oa":true,"landing_page_url":"https://doi.org/10.1214/009053607000000271","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-35/issue-5/Spatial-aggregation-of-local-likelihood-estimates-with-applications-to-classification/10.1214/009053607000000271.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/W2012004107.pdf","grobid_xml":"https://content.openalex.org/works/W2012004107.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W138682821","https://openalex.org/W1494947645","https://openalex.org/W1575244755","https://openalex.org/W1597926580","https://openalex.org/W1963509555","https://openalex.org/W1984140225","https://openalex.org/W1986360843","https://openalex.org/W1995514448","https://openalex.org/W1997927050","https://openalex.org/W1998695078","https://openalex.org/W2000318912","https://openalex.org/W2000953144","https://openalex.org/W2012004107","https://openalex.org/W2050284024","https://openalex.org/W2062772460","https://openalex.org/W2073123088","https://openalex.org/W2093381735","https://openalex.org/W2101675718","https://openalex.org/W2155729182","https://openalex.org/W2168227362","https://openalex.org/W2796930163","https://openalex.org/W2914369697","https://openalex.org/W3124371155","https://openalex.org/W4229576166","https://openalex.org/W4233748032","https://openalex.org/W6684452406"],"related_works":["https://openalex.org/W143502885","https://openalex.org/W42113618","https://openalex.org/W2103468410","https://openalex.org/W1485223389","https://openalex.org/W2040597492","https://openalex.org/W2013882407","https://openalex.org/W2901843708","https://openalex.org/W4236777572","https://openalex.org/W1981436518","https://openalex.org/W2161099019"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,16,38,48,69,95],"new":[4,49,70],"method":[5,35],"for":[6,128],"spatially":[7],"adaptive":[8],"local":[9,41],"(constant)":[10],"likelihood":[11,42],"estimation":[12],"which":[13],"applies":[14],"to":[15,46,119,124,143],"broad":[17],"class":[18],"of":[19,33,40,56,58,76,84,97,104,132,136],"nonparametric":[20],"models,":[21],"including":[22],"the":[23,34,59,74,77,81,85,89,102,105,125,129,137,144],"Gaussian,":[24],"Poisson":[25],"and":[26,156],"binary":[27],"response":[28],"models.":[29],"The":[30,134],"main":[31],"idea":[32],"is,":[36,117],"given":[37,130],"sequence":[39],"estimates":[43],"(\u201cweak\u201d":[44],"estimates),":[45],"construct":[47],"aggregated":[50,106],"estimate":[51,87],"whose":[52],"pointwise":[53],"risk":[54,61,116,127],"is":[55,139],"order":[57],"smallest":[60,126],"among":[62],"all":[63],"\u201cweak\u201d":[64],"estimates.":[65,133],"We":[66,93],"also":[67],"propose":[68],"approach":[71],"toward":[72],"selecting":[73],"parameters":[75],"procedure":[78,138],"by":[79,141],"providing":[80],"prescribed":[82],"behavior":[83],"resulting":[86],"in":[88,154],"simple":[90],"parametric":[91],"situation.":[92],"establish":[94],"number":[96],"important":[98],"theoretical":[99],"results":[100],"concerning":[101],"optimality":[103],"estimate.":[107],"In":[108],"particular,":[109],"our":[110],"\u201coracle\u201d":[111],"result":[112],"claims":[113],"that":[114],"its":[115,151],"up":[118],"some":[120],"logarithmic":[121],"multiplier,":[122],"equal":[123],"family":[131],"performance":[135,153],"illustrated":[140],"application":[142],"classification":[145],"problem.":[146],"A":[147],"numerical":[148],"study":[149],"demonstrates":[150],"reasonable":[152],"simulated":[155],"real-life":[157],"examples.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}