{"id":"https://openalex.org/W3099812441","doi":null,"title":"ADAPTIVE ESTIMATION UNDER SINGLE-INDEX CONSTRAINT IN A REGRESSION MODEL1","display_name":"ADAPTIVE ESTIMATION UNDER SINGLE-INDEX CONSTRAINT IN A REGRESSION MODEL1","publication_year":2016,"publication_date":"2016-08-18","ids":{"openalex":"https://openalex.org/W3099812441","mag":"3099812441"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.770.4235","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.770.4235","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/1304.7668.pdf","raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028786617","display_name":"Oleg Lepski","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Oleg Lepski","raw_affiliation_strings":["I2M - Institut de Math\u00e9matiques de Marseille (Centre de Math\u00e9matiques et Informatique (CMI)\r\nTechnop\u00f4le Ch\u00e2teau-Gombert\r\n39, rue Fr\u00e9d\u00e9ric Joliot Curie\r\n13453 Marseille Cedex 13  - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"I2M - Institut de Math\u00e9matiques de Marseille (Centre de Math\u00e9matiques et Informatique (CMI)\r\nTechnop\u00f4le Ch\u00e2teau-Gombert\r\n39, rue Fr\u00e9d\u00e9ric Joliot Curie\r\n13453 Marseille Cedex 13  - France)","institution_ids":["https://openalex.org/I4210138206"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064997487","display_name":"Nora Serdyukova","orcid":"https://orcid.org/0000-0001-8310-8858","observed_orcids":["https://orcid.org/0000-0001-8310-8858"]},"institutions":[{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nora Serdyukova","raw_affiliation_strings":["I2M - Institut de Math\u00e9matiques de Marseille (Centre de Math\u00e9matiques et Informatique (CMI)\r\nTechnop\u00f4le Ch\u00e2teau-Gombert\r\n39, rue Fr\u00e9d\u00e9ric Joliot Curie\r\n13453 Marseille Cedex 13  - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"I2M - Institut de Math\u00e9matiques de Marseille (Centre de Math\u00e9matiques et Informatique (CMI)\r\nTechnop\u00f4le Ch\u00e2teau-Gombert\r\n39, rue Fr\u00e9d\u00e9ric Joliot Curie\r\n13453 Marseille Cedex 13  - France)","institution_ids":["https://openalex.org/I4210138206"]}]},{"author_position":"last","author":{"id":null,"display_name":"Aix-marseille Universite \u0301","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aix-marseille Universite \u0301","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9937000274658203,"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":0.9937000274658203,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.0012000000569969416,"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":0.000699999975040555,"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/adaptive-estimation","display_name":"adaptive estimation","score":0.7929999828338623},{"id":"https://openalex.org/keywords/single-index-model","display_name":"single index model","score":0.8180000185966492},{"id":"https://openalex.org/keywords/random-design","display_name":"random design","score":0.5809999704360962},{"id":"https://openalex.org/keywords/kernel-density-estimation","display_name":"kernel density estimation","score":0.7289999723434448},{"id":"https://openalex.org/keywords/oracle-inequalities","display_name":"oracle inequalities","score":0.781000018119812},{"id":"https://openalex.org/keywords/link-function-estimation","display_name":"link function estimation","score":0.6480000019073486},{"id":"https://openalex.org/keywords/holder-classes","display_name":"H\u00f6lder classes","score":0.8009999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8468355536460876},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7978609204292297},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7285599112510681},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6190354824066162},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.5762406587600708},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4815671443939209},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.4584408104419708},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4551427960395813},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.44885915517807007},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.44519925117492676},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.43692493438720703},{"id":"https://openalex.org/C2780617739","wikidata":"https://www.wikidata.org/wiki/Q4680738","display_name":"Adaptive estimator","level":3,"score":0.41372257471084595},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.383733332157135},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37373632192611694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11379453539848328},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.770.4235","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.770.4235","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/1304.7668.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W191129667","https://openalex.org/W1515878031","https://openalex.org/W1968172088","https://openalex.org/W1972568734","https://openalex.org/W1972805551","https://openalex.org/W1974801771","https://openalex.org/W1981961957","https://openalex.org/W1986360843","https://openalex.org/W1986983255","https://openalex.org/W1992676028","https://openalex.org/W2009689404","https://openalex.org/W2029838749","https://openalex.org/W2049012892","https://openalex.org/W2074148972","https://openalex.org/W2092891775","https://openalex.org/W2098910318","https://openalex.org/W2103605411","https://openalex.org/W2141195893","https://openalex.org/W2156218552","https://openalex.org/W2323602348","https://openalex.org/W2330374167","https://openalex.org/W2462965978","https://openalex.org/W4249152756"],"related_works":["https://openalex.org/W2094217278","https://openalex.org/W2282669949","https://openalex.org/W2952903069","https://openalex.org/W1551697536","https://openalex.org/W1881649853","https://openalex.org/W7098325627","https://openalex.org/W2462965978","https://openalex.org/W2171846551","https://openalex.org/W7095323983","https://openalex.org/W7116446859"],"abstract_inverted_index":{"The":[0],"problem":[1],"of":[2,38,47,69,85,94],"adaptive":[3,89],"multivariate":[4],"function":[5,41,73],"estimation":[6,25,90],"in":[7,60],"the":[8,19,31,36,39,67,71,78,83],"single-index":[9],"regression":[10],"model":[11],"with":[12],"random":[13],"design":[14],"and":[15,35,87,96],"weak":[16],"assumptions":[17],"on":[18],"noise":[20],"is":[21,51,63],"investigated.":[22],"A":[23],"novel":[24],"procedure":[26],"that":[27],"adapts":[28],"simultaneously":[29],"to":[30,65,82],"unknown":[32],"index":[33],"vector":[34],"smoothness":[37],"link":[40],"by":[42],"selecting":[43],"from":[44],"a":[45,55,92],"family":[46],"specific":[48],"kernel":[49],"estimators":[50],"proposed.":[52],"We":[53],"establish":[54],"pointwise":[56,86],"oracle":[57,75],"inequality":[58],"which,":[59],"its":[61],"turn,":[62],"used":[64],"judge":[66],"quality":[68],"estimating":[70],"entire":[72],"(``global''":[74],"inequality).":[76],"Both":[77],"results":[79],"are":[80],"applied":[81],"problems":[84],"global":[88],"over":[91],"collection":[93],"H\\\"{o}lder":[95],"Nikol'skii":[97],"functional":[98],"classes,":[99],"respectively.":[100]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2020-11-23T00:00:00"}