{"id":"https://openalex.org/W2523442049","doi":"https://doi.org/10.1109/tac.2016.2612543","title":"Minimax Lower Bound and Optimal Estimation of Convex Functions in the Sup-Norm","display_name":"Minimax Lower Bound and Optimal Estimation of Convex Functions in the Sup-Norm","publication_year":2016,"publication_date":"2016-09-21","ids":{"openalex":"https://openalex.org/W2523442049","doi":"https://doi.org/10.1109/tac.2016.2612543","mag":"2523442049"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2016.2612543","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2612543","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5078508937","display_name":"Teresa M. Lebair","orcid":null},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Teresa M. Lebair","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013733463","display_name":"Jinglai Shen","orcid":"https://orcid.org/0000-0003-2172-4182"},"institutions":[{"id":"https://openalex.org/I79272384","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78","country_code":"US","type":"education","lineage":["https://openalex.org/I79272384"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jinglai Shen","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Maryland, Baltimore County, MD, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Maryland, Baltimore County, MD, USA","institution_ids":["https://openalex.org/I79272384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100753199","display_name":"Wang Xiao","orcid":"https://orcid.org/0000-0003-2305-2666"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiao Wang","raw_affiliation_strings":["Department of Statistics, Purdue University, West Lafayette, IN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078508937"],"corresponding_institution_ids":["https://openalex.org/I145311948"],"apc_list":null,"apc_paid":null,"fwci":0.6079,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69355025,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"62","issue":"7","first_page":"3482","last_page":"3487"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.968500018119812,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.968500018119812,"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":0.9345999956130981,"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"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9236000180244446,"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/mathematics","display_name":"Mathematics","score":0.7707382440567017},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.7585529088973999},{"id":"https://openalex.org/keywords/uniform-norm","display_name":"Uniform norm","score":0.6870867013931274},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5266401767730713},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5228957533836365},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5208573937416077},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5129830241203308},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.507808268070221},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.49265891313552856},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.47930875420570374},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.466169148683548},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4644261598587036},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.45142143964767456},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.44733768701553345},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.4378906488418579},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.434828519821167},{"id":"https://openalex.org/keywords/minimax-approximation-algorithm","display_name":"Minimax approximation algorithm","score":0.42755335569381714},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.41428524255752563},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.38521069288253784},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3777627944946289},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18896594643592834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13933652639389038},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11409458518028259}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7707382440567017},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7585529088973999},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.6870867013931274},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5266401767730713},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5228957533836365},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5208573937416077},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5129830241203308},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.507808268070221},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.49265891313552856},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.47930875420570374},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.466169148683548},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4644261598587036},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.45142143964767456},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.44733768701553345},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.4378906488418579},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.434828519821167},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.42755335569381714},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.41428524255752563},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38521069288253784},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3777627944946289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18896594643592834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13933652639389038},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11409458518028259},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2016.2612543","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2612543","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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":33,"referenced_works":["https://openalex.org/W9200771","https://openalex.org/W562843364","https://openalex.org/W786265215","https://openalex.org/W1511694993","https://openalex.org/W1973429478","https://openalex.org/W1979663407","https://openalex.org/W1985244441","https://openalex.org/W2023912140","https://openalex.org/W2028396654","https://openalex.org/W2031932449","https://openalex.org/W2036986658","https://openalex.org/W2038845890","https://openalex.org/W2058729597","https://openalex.org/W2066649525","https://openalex.org/W2068287590","https://openalex.org/W2099111195","https://openalex.org/W2099942006","https://openalex.org/W2110781925","https://openalex.org/W2121554703","https://openalex.org/W2121904620","https://openalex.org/W2122818263","https://openalex.org/W2125128574","https://openalex.org/W2129623910","https://openalex.org/W2131590629","https://openalex.org/W2143558629","https://openalex.org/W2159263703","https://openalex.org/W2165412696","https://openalex.org/W2478708596","https://openalex.org/W2962703606","https://openalex.org/W3217015688","https://openalex.org/W6658471284","https://openalex.org/W6678471722","https://openalex.org/W6684617389"],"related_works":["https://openalex.org/W3157591918","https://openalex.org/W2962921834","https://openalex.org/W3112089849","https://openalex.org/W3171267590","https://openalex.org/W3206232691","https://openalex.org/W3203586630","https://openalex.org/W2035984587","https://openalex.org/W4385292186","https://openalex.org/W2356261519","https://openalex.org/W2071919366"],"abstract_inverted_index":{"Estimation":[0],"of":[1,21,34,62,89,96,116,128],"convex":[2,13,36,65,97,122],"functions":[3,37,66,98],"finds":[4],"broad":[5],"applications":[6],"in":[7,38,48,67,130],"science":[8],"and":[9,105],"engineering;":[10],"however,":[11],"the":[12,17,30,49,68,79,86,92,100,112,117,125,131],"shape":[14],"constraint":[15],"complicates":[16],"asymptotic":[18],"performance":[19],"analysis":[20],"such":[22],"estimators.":[23],"This":[24,71],"technical":[25,109],"note":[26,110],"is":[27,55],"devoted":[28],"to":[29,85],"minimax":[31,45,80,93,119],"optimal":[32,87,118],"estimation":[33,123],"univariate":[35],"a":[39,44,59,75],"given":[40],"H\u00f6lder":[41,69,101],"class.":[42,70],"Particularly,":[43],"lower":[46],"bound":[47],"supremum":[50],"norm":[51],"(or":[52],"simply":[53],"sup-norm)":[54],"established":[56],"by":[57],"constructing":[58],"novel":[60],"family":[61],"piecewise":[63],"quadratic":[64],"result,":[72],"along":[73],"with":[74,99],"recent":[76],"result":[77],"on":[78,124],"upper":[81],"bound,":[82],"gives":[83],"rise":[84],"rate":[88],"convergence":[90],"for":[91,121],"sup-norm":[94],"risk":[95,120],"order":[102],"between":[103],"one":[104],"two.":[106],"The":[107],"present":[108],"provides":[111],"first":[113],"rigorous":[114],"justification":[115],"entire":[126],"interval":[127],"interest":[129],"sup-norm.":[132]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
