{"id":"https://openalex.org/W2014688984","doi":"https://doi.org/10.1214/009053604000001066","title":"Square root penalty: Adaptation to the margin in classification and in edge estimation","display_name":"Square root penalty: Adaptation to the margin in classification and in edge estimation","publication_year":2005,"publication_date":"2005-06-01","ids":{"openalex":"https://openalex.org/W2014688984","doi":"https://doi.org/10.1214/009053604000001066","mag":"2014688984"},"language":"en","primary_location":{"id":"doi:10.1214/009053604000001066","doi":"https://doi.org/10.1214/009053604000001066","is_oa":true,"landing_page_url":"https://doi.org/10.1214/009053604000001066","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-33/issue-3/Square-root-penalty--Adaptation-to-the-margin-in-classification/10.1214/009053604000001066.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"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-33/issue-3/Square-root-penalty--Adaptation-to-the-margin-in-classification/10.1214/009053604000001066.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112866084","display_name":"Alexandre B. Tsybakov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]},{"id":"https://openalex.org/I4210147464","display_name":"Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires","ror":"https://ror.org/04hjc7403","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I40434647","https://openalex.org/I4210124654","https://openalex.org/I4210141950","https://openalex.org/I4210147464","https://openalex.org/I4387155306","https://openalex.org/I48825208"]},{"id":"https://openalex.org/I4405264447","display_name":"Universit\u00e9 Pierre-et-Marie-Curie","ror":"https://ror.org/01yvrd251","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081","https://openalex.org/I4405264447"]}],"countries":["FR","NL"],"is_corresponding":false,"raw_author_name":"A. B. Tsybakov","raw_affiliation_strings":["LABORATOIRE DE PROBABILIT\u00c9S ET MOD\u00c8LES AL\u00c9ATOIRES UNIVERSIT\u00c9 PARIS VI 4 PLACE JUSSIEU CASE 188 F-75252 PARIS C\u00c9DEX 05 FRANCE","Universit\u00e9 Paris VI and University of Leiden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LABORATOIRE DE PROBABILIT\u00c9S ET MOD\u00c8LES AL\u00c9ATOIRES UNIVERSIT\u00c9 PARIS VI 4 PLACE JUSSIEU CASE 188 F-75252 PARIS C\u00c9DEX 05 FRANCE","institution_ids":["https://openalex.org/I4210147464"]},{"raw_affiliation_string":"Universit\u00e9 Paris VI and University of Leiden","institution_ids":["https://openalex.org/I121797337","https://openalex.org/I4405264447"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033661683","display_name":"Sara van de Geer","orcid":"https://orcid.org/0000-0001-7181-2872","observed_orcids":["https://orcid.org/0000-0001-7181-2872"]},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]},{"id":"https://openalex.org/I4405264447","display_name":"Universit\u00e9 Pierre-et-Marie-Curie","ror":"https://ror.org/01yvrd251","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081","https://openalex.org/I4405264447"]}],"countries":["FR","NL"],"is_corresponding":false,"raw_author_name":"S. A. van de Geer","raw_affiliation_strings":["MATHEMATICAL INSTITUTE UNIVERSITY OF LEIDEN P.O. BOX 9512 2300 RA LEIDEN THE NETHERLANDS","Universit\u00e9 Paris VI and University of Leiden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MATHEMATICAL INSTITUTE UNIVERSITY OF LEIDEN P.O. BOX 9512 2300 RA LEIDEN THE NETHERLANDS","institution_ids":["https://openalex.org/I121797337"]},{"raw_affiliation_string":"Universit\u00e9 Paris VI and University of Leiden","institution_ids":["https://openalex.org/I121797337","https://openalex.org/I4405264447"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.4975,"has_fulltext":true,"cited_by_count":57,"citation_normalized_percentile":{"value":0.97708062,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"33","issue":"3","first_page":"1203","last_page":"1224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9970999956130981,"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":0.9970999956130981,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.0006000000284984708,"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"}},{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.0003000000142492354,"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/binary-classification","display_name":"binary classification","score":0.8479999899864197},{"id":"https://openalex.org/keywords/excess-risk","display_name":"excess risk","score":0.824999988079071},{"id":"https://openalex.org/keywords/optimal-convergence-rates","display_name":"optimal convergence rates","score":0.8209999799728394},{"id":"https://openalex.org/keywords/edge-estimation","display_name":"edge estimation","score":0.8119999766349792},{"id":"https://openalex.org/keywords/adaptive-estimation","display_name":"adaptive estimation","score":0.6039999723434448}],"concepts":[{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.7419999837875366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7299000024795532},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6796000003814697},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5712000131607056},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5648000240325928},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4952000081539154},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.38830000162124634},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3853999972343445},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38440001010894775},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.38429999351501465},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.36149999499320984},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.32919999957084656},{"id":"https://openalex.org/C66905080","wikidata":"https://www.wikidata.org/wiki/Q17005494","display_name":"Binary classification","level":3,"score":0.3181999921798706},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C139807058","wikidata":"https://www.wikidata.org/wiki/Q352374","display_name":"Adaptation (eye)","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.289900004863739},{"id":"https://openalex.org/C107321475","wikidata":"https://www.wikidata.org/wiki/Q5374254","display_name":"Empirical risk minimization","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C31441030","wikidata":"https://www.wikidata.org/wiki/Q4291882","display_name":"Least absolute deviations","level":3,"score":0.27630001306533813},{"id":"https://openalex.org/C2776434776","wikidata":"https://www.wikidata.org/wiki/Q19246213","display_name":"Domain adaptation","level":3,"score":0.27070000767707825},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2597000002861023},{"id":"https://openalex.org/C193536780","wikidata":"https://www.wikidata.org/wiki/Q1513153","display_name":"Edge detection","level":4,"score":0.2572000026702881},{"id":"https://openalex.org/C2780617739","wikidata":"https://www.wikidata.org/wiki/Q4680738","display_name":"Adaptive estimator","level":3,"score":0.2540999948978424}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1214/009053604000001066","doi":"https://doi.org/10.1214/009053604000001066","is_oa":true,"landing_page_url":"https://doi.org/10.1214/009053604000001066","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-33/issue-3/Square-root-penalty--Adaptation-to-the-margin-in-classification/10.1214/009053604000001066.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:math/0507422","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0507422","pdf_url":"https://arxiv.org/pdf/math/0507422","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:CULeuclid:euclid.aos/1120224100","doi":null,"is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.aos/1120224100","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:10.1214/009053604000001066","doi":"https://doi.org/10.1214/009053604000001066","is_oa":true,"landing_page_url":"https://doi.org/10.1214/009053604000001066","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-33/issue-3/Square-root-penalty--Adaptation-to-the-margin-in-classification/10.1214/009053604000001066.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/W2014688984.pdf","grobid_xml":"https://content.openalex.org/works/W2014688984.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1495241956","https://openalex.org/W1498939395","https://openalex.org/W1564947197","https://openalex.org/W1608733719","https://openalex.org/W1968053885","https://openalex.org/W1982032418","https://openalex.org/W1996268356","https://openalex.org/W2043919728","https://openalex.org/W2049393399","https://openalex.org/W2087258353","https://openalex.org/W2092530991","https://openalex.org/W2101718974","https://openalex.org/W2163150561","https://openalex.org/W2487926728","https://openalex.org/W3105849782","https://openalex.org/W4205354563","https://openalex.org/W4253012481"],"related_works":[],"abstract_inverted_index":{"We":[0,12,52],"consider":[1],"the":[2,7,34,49,62],"problem":[3,63],"of":[4,31,64],"adaptation":[5],"to":[6,24],"margin":[8],"in":[9],"binary":[10],"classification.":[11],"suggest":[13],"a":[14,25],"penalized":[15],"empirical":[16],"risk":[17],"minimization":[18],"classifier":[19],"that":[20,37,40,54],"adaptively":[21],"attains,":[22],"up":[23],"logarithmic":[26],"factor,":[27],"fast":[28],"optimal":[29],"rates":[30,39],"convergence":[32],"for":[33,61],"excess":[35],"risk,":[36],"is,":[38],"can":[41],"be":[42],"faster":[43],"than":[44],"n\u22121/2,":[45],"where":[46],"n":[47],"is":[48],"sample":[50],"size.":[51],"show":[53],"our":[55],"method":[56],"also":[57],"gives":[58],"adaptive":[59],"estimators":[60],"edge":[65],"estimation.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}
