{"id":"https://openalex.org/W2067117017","doi":"https://doi.org/10.1214/aos/1176325500","title":"On Good Deterministic Smoothing Sequences for Kernel Density Estimates","display_name":"On Good Deterministic Smoothing Sequences for Kernel Density Estimates","publication_year":1994,"publication_date":"1994-06-01","ids":{"openalex":"https://openalex.org/W2067117017","doi":"https://doi.org/10.1214/aos/1176325500","mag":"2067117017"},"language":"en","primary_location":{"id":"doi:10.1214/aos/1176325500","doi":"https://doi.org/10.1214/aos/1176325500","is_oa":true,"landing_page_url":"https://doi.org/10.1214/aos/1176325500","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-22/issue-2/On-Good-Deterministic-Smoothing-Sequences-for-Kernel-Density-Estimates/10.1214/aos/1176325500.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-22/issue-2/On-Good-Deterministic-Smoothing-Sequences-for-Kernel-Density-Estimates/10.1214/aos/1176325500.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070394029","display_name":"Luc Devroye","orcid":"https://orcid.org/0009-0001-4330-8991","observed_orcids":["https://orcid.org/0009-0001-4330-8991"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Luc Devroye","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5070394029"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6618,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.8594306,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"2","first_page":"886","last_page":"889"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.6596999764442444,"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/T13500","display_name":"Probability and Statistical Research","score":0.6596999764442444,"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/T10136","display_name":"Statistical Methods and Inference","score":0.2808000147342682,"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":0.015599999576807022,"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/kernel-density-estimation","display_name":"kernel density estimation","score":0.9750000238418579},{"id":"https://openalex.org/keywords/probabilistic-methods","display_name":"probabilistic methods","score":0.7419999837875366},{"id":"https://openalex.org/keywords/asymptotic-optimality","display_name":"asymptotic optimality","score":0.5090000033378601},{"id":"https://openalex.org/keywords/nonparametric-density-estimation","display_name":"nonparametric density estimation","score":0.6489999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8808001279830933},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7042679786682129},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6248874664306641},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5944912433624268},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.49559485912323},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.46577781438827515},{"id":"https://openalex.org/C27406209","wikidata":"https://www.wikidata.org/wiki/Q6394203","display_name":"Kernel smoother","level":5,"score":0.4201134741306305},{"id":"https://openalex.org/C183212220","wikidata":"https://www.wikidata.org/wiki/Q3345669","display_name":"Heat kernel","level":2,"score":0.415221631526947},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3266291618347168},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.28408098220825195},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2598195970058441},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2500775456428528},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05530098080635071},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1214/aos/1176325500","doi":"https://doi.org/10.1214/aos/1176325500","is_oa":true,"landing_page_url":"https://doi.org/10.1214/aos/1176325500","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-22/issue-2/On-Good-Deterministic-Smoothing-Sequences-for-Kernel-Density-Estimates/10.1214/aos/1176325500.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/1176325500","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.aos/1176325500","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/1176325500","doi":"https://doi.org/10.1214/aos/1176325500","is_oa":true,"landing_page_url":"https://doi.org/10.1214/aos/1176325500","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-22/issue-2/On-Good-Deterministic-Smoothing-Sequences-for-Kernel-Density-Estimates/10.1214/aos/1176325500.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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2067117017.pdf","grobid_xml":"https://content.openalex.org/works/W2067117017.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W44379224","https://openalex.org/W1987413591","https://openalex.org/W2014268383","https://openalex.org/W2044595014","https://openalex.org/W2057443396","https://openalex.org/W2068871408","https://openalex.org/W2072227363","https://openalex.org/W2118020555","https://openalex.org/W3023646433"],"related_works":["https://openalex.org/W2552416899","https://openalex.org/W2021569877","https://openalex.org/W2999721917","https://openalex.org/W4287906215","https://openalex.org/W2920855166","https://openalex.org/W1658186381","https://openalex.org/W4205267905","https://openalex.org/W4206381862","https://openalex.org/W3142731338","https://openalex.org/W3149448578"],"abstract_inverted_index":{"We":[0],"use":[1],"the":[2,11],"probabilistic":[3],"method":[4],"to":[5],"show":[6],"that":[7],"if":[8],"$f_{nh}$":[9],"is":[10],"standard":[12],"kernel":[13],"estimate":[14],"with":[15],"smoothing":[16],"factor":[17],"$h$,":[18],"then":[19],"there":[20],"exists":[21],"a":[22],"deterministic":[23],"sequence":[24],"$h_n$":[25],"such":[26],"that,":[27],"for":[28],"all":[29],"densities,":[30],"$\\operatornamewithlimits{\\lim\\inf}_{n\\rightarrow\\infty}":[31],"\\frac{\\mathbf{E}":[32],"\\int":[33,38],"|f_{nh_n}":[34],"-":[35,40],"f|}{\\inf_h":[36],"\\mathbf{E}":[37],"|f_{nh}":[39],"f|}":[41],"=":[42],"1.$":[43]},"counts_by_year":[],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2025-10-10T00:00:00"}