{"id":"https://openalex.org/W4293483762","doi":"https://doi.org/10.1214/22-aos2188","title":"Nonregular and minimax estimation of individualized thresholds in high dimension with binary responses","display_name":"Nonregular and minimax estimation of individualized thresholds in high dimension with binary responses","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W4293483762","doi":"https://doi.org/10.1214/22-aos2188"},"language":"en","primary_location":{"id":"doi:10.1214/22-aos2188","doi":"https://doi.org/10.1214/22-aos2188","is_oa":true,"landing_page_url":"https://doi.org/10.1214/22-aos2188","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-50/issue-4/Nonregular-and-minimax-estimation-of-individualized-thresholds-in-high-dimension/10.1214/22-AOS2188.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","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-50/issue-4/Nonregular-and-minimax-estimation-of-individualized-thresholds-in-high-dimension/10.1214/22-AOS2188.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003058598","display_name":"Huijie Feng","orcid":"https://orcid.org/0000-0002-1835-6190","observed_orcids":["https://orcid.org/0000-0002-1835-6190"]},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Huijie Feng","raw_affiliation_strings":["Department of Statistics and Data Science, Cornell University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, Cornell University","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070406375","display_name":"Yang Ning","orcid":"https://orcid.org/0000-0001-6877-9231","observed_orcids":["https://orcid.org/0000-0001-6877-9231"]},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yang Ning","raw_affiliation_strings":["Department of Statistics and Data Science, Cornell University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, Cornell University","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083969121","display_name":"Jiwei Zhao","orcid":"https://orcid.org/0000-0002-9298-9412","observed_orcids":["https://orcid.org/0000-0002-9298-9412"]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiwei Zhao","raw_affiliation_strings":["Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0613,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.77635783,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":92,"max":96},"biblio":{"volume":"50","issue":"4","first_page":"2284","last_page":"2305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.0,"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/high-dimensional-estimation","display_name":"high-dimensional estimation","score":0.5879999995231628},{"id":"https://openalex.org/keywords/binary-outcomes","display_name":"binary outcomes","score":0.7089999914169312},{"id":"https://openalex.org/keywords/minimax-rate-optimality","display_name":"minimax rate optimality","score":0.7269999980926514},{"id":"https://openalex.org/keywords/empirical-risk-minimization","display_name":"empirical risk minimization","score":0.9380000233650208},{"id":"https://openalex.org/keywords/fisher-consistency","display_name":"Fisher consistency","score":0.7630000114440918},{"id":"https://openalex.org/keywords/path-following-methods","display_name":"path-following algorithm","score":0.7419999837875366},{"id":"https://openalex.org/keywords/sign-function","display_name":"sign function","score":0.3840000033378601},{"id":"https://openalex.org/keywords/sparsity","display_name":"sparsity","score":0.3790000081062317}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8314090967178345},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7561997175216675},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6313983201980591},{"id":"https://openalex.org/C107321475","wikidata":"https://www.wikidata.org/wiki/Q5374254","display_name":"Empirical risk minimization","level":2,"score":0.5287454128265381},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49021416902542114},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.4657386541366577},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.46503016352653503},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45698311924934387},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.45245561003685},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43162092566490173},{"id":"https://openalex.org/C119043178","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Covariate","level":2,"score":0.422615647315979},{"id":"https://openalex.org/C31441030","wikidata":"https://www.wikidata.org/wiki/Q4291882","display_name":"Least absolute deviations","level":3,"score":0.4111623764038086},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3536769151687622},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2567393481731415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.100131094455719},{"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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":3,"locations":[{"id":"doi:10.1214/22-aos2188","doi":"https://doi.org/10.1214/22-aos2188","is_oa":true,"landing_page_url":"https://doi.org/10.1214/22-aos2188","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-50/issue-4/Nonregular-and-minimax-estimation-of-individualized-thresholds-in-high-dimension/10.1214/22-AOS2188.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:1905.10888","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.10888","pdf_url":"https://arxiv.org/pdf/1905.10888","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":"doi:10.48550/arxiv.1905.10888","doi":"https://doi.org/10.48550/arxiv.1905.10888","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.10888","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1214/22-aos2188","doi":"https://doi.org/10.1214/22-aos2188","is_oa":true,"landing_page_url":"https://doi.org/10.1214/22-aos2188","pdf_url":"https://projecteuclid.org/journals/annals-of-statistics/volume-50/issue-4/Nonregular-and-minimax-estimation-of-individualized-thresholds-in-high-dimension/10.1214/22-AOS2188.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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2348671469","display_name":"A Robust and Efficient Statistical Framework for Handling Missing-Not-At-Random Data in Patient Reported Outcomes and Beyond","funder_award_id":"2122074","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6273723344","display_name":"CDS&E: Graph-Based Learning and Uncertainty Quantification for Large-Scale Complex Data","funder_award_id":"1854637","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7737154021","display_name":"CAREER: High-Dimensional M-Estimation Under Nonstandard Conditions","funder_award_id":"1941945","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309434","display_name":"University of Wisconsin-Madison","ror":"https://ror.org/01y2jtd41"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4293483762.pdf","grobid_xml":"https://content.openalex.org/works/W4293483762.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1511694993","https://openalex.org/W1538269260","https://openalex.org/W1874232560","https://openalex.org/W1894828066","https://openalex.org/W1981961957","https://openalex.org/W1982032418","https://openalex.org/W1983697434","https://openalex.org/W1994857208","https://openalex.org/W1995642533","https://openalex.org/W2010353172","https://openalex.org/W2022050125","https://openalex.org/W2023163512","https://openalex.org/W2030161963","https://openalex.org/W2030843733","https://openalex.org/W2046675234","https://openalex.org/W2049393399","https://openalex.org/W2060430274","https://openalex.org/W2063978378","https://openalex.org/W2065856880","https://openalex.org/W2066986830","https://openalex.org/W2068221105","https://openalex.org/W2089394015","https://openalex.org/W2101095383","https://openalex.org/W2101157574","https://openalex.org/W2111084117","https://openalex.org/W2111992537","https://openalex.org/W2112090892","https://openalex.org/W2116039321","https://openalex.org/W2129131372","https://openalex.org/W2137911812","https://openalex.org/W2141195893","https://openalex.org/W2146782960","https://openalex.org/W2151825876","https://openalex.org/W2152575748","https://openalex.org/W2159700154","https://openalex.org/W2161227280","https://openalex.org/W2397246475","https://openalex.org/W2728289232","https://openalex.org/W2756630952","https://openalex.org/W2796930163","https://openalex.org/W2963943067","https://openalex.org/W3048221291","https://openalex.org/W4247571494"],"related_works":["https://openalex.org/W1544320188","https://openalex.org/W3018524337","https://openalex.org/W2808684295","https://openalex.org/W2106086802","https://openalex.org/W7213596032","https://openalex.org/W6940483163","https://openalex.org/W7168138977","https://openalex.org/W2589365575","https://openalex.org/W2999897127","https://openalex.org/W7131226405"],"abstract_inverted_index":{"Given":[0],"a":[1,12,23,34,75,107,213,275],"large":[2],"number":[3],"of":[4,11,60,93,116,125,155,172,176,253,267],"covariates":[5,184],"Z,":[6],"we":[7,98,134,201,261],"consider":[8],"the":[9,29,39,45,49,61,69,85,91,94,117,123,126,137,153,159,164,170,173,179,183,196,204,223,226,242,257,263,268,280],"estimation":[10,92],"high-dimensional":[13,95],"parameter":[14,96],"\u03b8":[15,66,144],"in":[16,68,90,145,195,271],"an":[17,100,234],"individualized":[18],"linear":[19],"threshold":[20],"\u03b8TZ":[21],"for":[22,142,255],"continuous":[24],"variable":[25],"X,":[26],"which":[27],"minimizes":[28],"disagreement":[30],"between":[31],"sign(X\u2212\u03b8TZ)":[32],"and":[33,87,167,182,191,274],"binary":[35],"response":[36,180],"Y.":[37],"While":[38],"problem":[40,77],"can":[41],"be":[42],"formulated":[43],"into":[44],"M-estimation":[46],"framework,":[47],"minimizing":[48],"corresponding":[50],"empirical":[51,101],"risk":[52,102],"function":[53],"is":[54,72,120,129,148,152,158,163,169,189,207,219,238],"computationally":[55],"intractable":[56],"due":[57],"to":[58,79,131,212,221,225,240],"discontinuity":[59],"sign":[62],"function.":[63,112],"Moreover,":[64],"estimating":[65,143],"even":[67],"fixed-dimensional":[70],"setting":[71],"known":[73],"as":[74,122],"nonregular":[76],"leading":[78],"nonstandard":[80,190],"asymptotic":[81],"theory.":[82],"To":[83],"tackle":[84],"computational":[86],"theoretical":[88],"challenges":[89],"\u03b8,":[97,156],"propose":[99],"minimization":[103],"approach":[104],"based":[105],"on":[106],"regularized":[108],"smoothed":[109,127],"non-convex":[110],"loss":[111,128],"The":[113,186,216],"Fisher":[114],"consistency":[115],"proposed":[118,239,269],"method":[119,218],"guaranteed":[121],"bandwidth":[124],"shrunk":[130],"0.":[132],"Statistically,":[133],"show":[135,246],"that":[136,194,203,247],"finite":[138,264],"sample":[139,165,265],"error":[140],"bound":[141],"\u21132":[146],"norm":[147],"(slogd/n)\u03b2/(2\u03b2+1),":[149],"where":[150],"d":[151],"dimension":[154],"s":[157,229],"sparsity":[160,228],"level,":[161],"n":[162],"size":[166],"\u03b2":[168],"smoothness":[171,231],"conditional":[174],"density":[175],"X":[177],"given":[178],"Y":[181],"Z.":[185],"convergence":[187,254],"rate":[188,209,252],"slower":[192],"than":[193],"classical":[197],"Lasso":[198],"problems.":[199],"Furthermore,":[200],"prove":[202],"resulting":[205],"estimator":[206,270],"minimax":[208],"optimal":[210],"up":[211],"logarithmic":[214],"factor.":[215],"Lepski\u2019s":[217],"developed":[220],"achieve":[222],"adaption":[224],"unknown":[227],"or":[230],"\u03b2.":[232],"Computationally,":[233],"efficient":[235],"path-following":[236],"algorithm":[237,249],"compute":[241],"solution":[243],"path.":[244,259],"We":[245],"this":[248],"achieves":[250],"geometric":[251],"computing":[256],"whole":[258],"Finally,":[260],"evaluate":[262],"performance":[266],"simulation":[272],"studies":[273],"real":[276],"data":[277],"analysis":[278],"from":[279],"ChAMP":[281],"(Chondral":[282],"Lesions":[283],"And":[284],"Meniscus":[285],"Procedures)":[286],"Trial.":[287]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-08-29T00:00:00"}
