{"id":"https://openalex.org/W2028396654","doi":"https://doi.org/10.1137/120887837","title":"Uniform Convergence and Rate Adaptive Estimation of Convex Functions via Constrained Optimization","display_name":"Uniform Convergence and Rate Adaptive Estimation of Convex Functions via Constrained Optimization","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2028396654","doi":"https://doi.org/10.1137/120887837","mag":"2028396654"},"language":"en","primary_location":{"id":"doi:10.1137/120887837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120887837","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5061363420","display_name":"Xiao Wang","orcid":"https://orcid.org/0000-0002-0663-6865"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5013733463","display_name":"Jinglai Shen","orcid":"https://orcid.org/0000-0003-2172-4182"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinglai Shen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2599,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.81498829,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"51","issue":"4","first_page":"2753","last_page":"2787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9976999759674072,"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":0.9976999759674072,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8092584609985352},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.712277889251709},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6386235952377319},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5982707142829895},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.571341335773468},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"Uniform convergence","score":0.5408346056938171},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5214328169822693},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5164111256599426},{"id":"https://openalex.org/keywords/uniform-norm","display_name":"Uniform norm","score":0.47526925802230835},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.46841397881507874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45579278469085693},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.4269941747188568},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.41601333022117615},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4156275987625122},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.3674106001853943},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.349115252494812},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20793160796165466},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12439769506454468},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12142407894134521}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8092584609985352},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.712277889251709},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6386235952377319},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5982707142829895},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.571341335773468},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.5408346056938171},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5214328169822693},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5164111256599426},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.47526925802230835},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.46841397881507874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45579278469085693},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.4269941747188568},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.41601333022117615},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4156275987625122},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.3674106001853943},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.349115252494812},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20793160796165466},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12439769506454468},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12142407894134521},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120887837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120887837","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1966103153","https://openalex.org/W1972568734","https://openalex.org/W1974114003","https://openalex.org/W1979663407","https://openalex.org/W1985244441","https://openalex.org/W2033062730","https://openalex.org/W2034109182","https://openalex.org/W2036986658","https://openalex.org/W2037914955","https://openalex.org/W2038290750","https://openalex.org/W2038845890","https://openalex.org/W2054640142","https://openalex.org/W2058729597","https://openalex.org/W2063122409","https://openalex.org/W2071901068","https://openalex.org/W2079313454","https://openalex.org/W2082204445","https://openalex.org/W2082990111","https://openalex.org/W2093381735","https://openalex.org/W2121904620","https://openalex.org/W2122818263","https://openalex.org/W2123849716","https://openalex.org/W2141195893","https://openalex.org/W2143558629","https://openalex.org/W3103695676"],"related_works":["https://openalex.org/W2037246265","https://openalex.org/W2038298159","https://openalex.org/W1980964769","https://openalex.org/W2386875945","https://openalex.org/W2348579042","https://openalex.org/W2028201632","https://openalex.org/W833821816","https://openalex.org/W4361981423","https://openalex.org/W4297899479","https://openalex.org/W1588473452"],"abstract_inverted_index":{"This":[0,60],"paper":[1],"discusses":[2],"asymptotic":[3,27,53],"analysis":[4],"and":[5,19,26,42,110,123,142,162],"adaptive":[6,43,148],"design":[7],"of":[8,47,66,69,88,99,126,132,174],"convex":[9,31,49,117],"estimators":[10,33],"over":[11,134,178],"the":[12,16,20,48,84,93,97,116,129,135,139,143,156,175,179],"H\u00f6lder":[13,136,157,180],"class":[14,137],"under":[15,138,152],"sup-norm":[17,140],"risk":[18,22,141,169,177],"pointwise":[21,144],"using":[23,105],"constrained":[24,72,101],"optimization":[25,73,102],"statistical":[28,111],"techniques.":[29],"Specifically,":[30],"B-spline":[32,118],"are":[34,150],"proposed":[35],"to":[36],"achieve":[37,166],"uniform":[38,57,85,121],"optimal":[39,89,124],"convergence":[40,58,127],"rates":[41,125],"procedures.":[44],"The":[45],"presence":[46],"shape":[50],"constraint":[51],"complicates":[52],"performance":[54],"analysis,":[55],"particularly":[56],"analysis.":[59],"in":[61,92],"turn":[62],"requires":[63],"deep":[64],"understanding":[65],"a":[67,167,171],"family":[68],"size":[70],"varying":[71],"problems":[74],"on":[75,128],"spline":[76,90],"coefficients.":[77],"To":[78],"address":[79],"these":[80],"issues,":[81],"we":[82,113],"establish":[83],"Lipschitz":[86],"property":[87],"coefficients":[91],"$\\ell_\\infty$-norm":[94],"by":[95],"exploiting":[96],"structure":[98],"underlying":[100],"problems.":[103],"By":[104],"this":[106],"property,":[107],"polyhedral":[108],"theory,":[109],"techniques,":[112],"show":[114],"that":[115],"estimator":[119],"attains":[120],"consistency":[122],"entire":[130],"interval":[131],"interest":[133],"risk.":[145],"In":[146],"addition,":[147],"estimates":[149,165],"constructed":[151],"both":[153],"risks":[154],"when":[155],"exponent":[158],"is":[159],"between":[160],"one":[161],"two.":[163],"These":[164],"maximal":[168],"within":[170],"constant":[172],"factor":[173],"minimax":[176],"class.":[181]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}