{"id":"https://openalex.org/W2042542290","doi":"https://doi.org/10.1109/allerton.2013.6736695","title":"Nearly optimal sample size in hypothesis testing for high-dimensional regression","display_name":"Nearly optimal sample size in hypothesis testing for high-dimensional regression","publication_year":2013,"publication_date":"2013-10-01","ids":{"openalex":"https://openalex.org/W2042542290","doi":"https://doi.org/10.1109/allerton.2013.6736695","mag":"2042542290"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2013.6736695","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2013.6736695","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1311.0274","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010342958","display_name":"Adel Javanmard","orcid":"https://orcid.org/0000-0003-1934-8747"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Adel Javanmard","raw_affiliation_strings":["Department of Electrical Engineering, Stanford University","[Dept. of Electr. Eng., Stanford Univ., Stanford, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"[Dept. of Electr. Eng., Stanford Univ., Stanford, CA, USA]","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011999109","display_name":"Andrea Montanari","orcid":"https://orcid.org/0000-0002-0267-8574"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrea Montanari","raw_affiliation_strings":["Department of Electrical Engineering and Department of Statistics, Stanford University","[Dept. of Electr. Eng., Stanford Univ., Stanford, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Department of Statistics, Stanford University","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"[Dept. of Electr. Eng., Stanford Univ., Stanford, CA, USA]","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010342958"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":2.114,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.86204951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1427","last_page":"1434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9993000030517578,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/estimator","display_name":"Estimator","score":0.8057650327682495},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.728705108165741},{"id":"https://openalex.org/keywords/ordinary-least-squares","display_name":"Ordinary least squares","score":0.6936048865318298},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.6854197978973389},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.6122684478759766},{"id":"https://openalex.org/keywords/design-matrix","display_name":"Design matrix","score":0.6054664850234985},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.562937319278717},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.529115617275238},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.4759896993637085},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4688578248023987},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.43634361028671265},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35589247941970825},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19112488627433777}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8057650327682495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.728705108165741},{"id":"https://openalex.org/C99656134","wikidata":"https://www.wikidata.org/wiki/Q2912993","display_name":"Ordinary least squares","level":2,"score":0.6936048865318298},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.6854197978973389},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.6122684478759766},{"id":"https://openalex.org/C203233044","wikidata":"https://www.wikidata.org/wiki/Q5264358","display_name":"Design matrix","level":3,"score":0.6054664850234985},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.562937319278717},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.529115617275238},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.4759896993637085},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4688578248023987},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.43634361028671265},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35589247941970825},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19112488627433777},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/allerton.2013.6736695","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2013.6736695","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1311.0274","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.0274","pdf_url":"https://arxiv.org/pdf/1311.0274","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"mag:2042542290","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1311.0274.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1311.0274","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1311.0274","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1311.0274","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.0274","pdf_url":"https://arxiv.org/pdf/1311.0274","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1413667363","display_name":null,"funder_award_id":"FA9550-13-1-0036","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2276563837","display_name":null,"funder_award_id":"9550-13-1-0036","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6071252945","display_name":null,"funder_award_id":"FA9550-12","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6329851102","display_name":null,"funder_award_id":"FA9550-12-1-0411","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"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/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7999580237","display_name":null,"funder_award_id":"FA9550-12-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8624150147","display_name":"CAREER:  New Information Processing Techniques from Statistical Physics and Probability Theory","funder_award_id":"0743978","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8673047835","display_name":null,"funder_award_id":"FA9550-12-1-0411","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2042542290.pdf","grobid_xml":"https://content.openalex.org/works/W2042542290.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W2010824638","https://openalex.org/W2034260606","https://openalex.org/W2037228647","https://openalex.org/W2082029531","https://openalex.org/W2097209031","https://openalex.org/W2108275041","https://openalex.org/W2116581043","https://openalex.org/W2127300249","https://openalex.org/W2128235479","https://openalex.org/W2129131372","https://openalex.org/W2135046866","https://openalex.org/W2152204644","https://openalex.org/W2154972590","https://openalex.org/W2170929819","https://openalex.org/W2949884817","https://openalex.org/W2965497096","https://openalex.org/W3098834468","https://openalex.org/W3099550161","https://openalex.org/W3105340263","https://openalex.org/W3121832289","https://openalex.org/W4247571494"],"related_works":["https://openalex.org/W2128235479","https://openalex.org/W2069119359","https://openalex.org/W2363252802","https://openalex.org/W2346798022","https://openalex.org/W3105340263","https://openalex.org/W2116581043","https://openalex.org/W1579207355","https://openalex.org/W2755149690","https://openalex.org/W3124442975","https://openalex.org/W2962710557","https://openalex.org/W1822188645","https://openalex.org/W1837783201","https://openalex.org/W2807765075","https://openalex.org/W3102567422","https://openalex.org/W1520698879","https://openalex.org/W2762307552","https://openalex.org/W1979642929","https://openalex.org/W3194416953","https://openalex.org/W340056678","https://openalex.org/W3098834468"],"abstract_inverted_index":{"We":[0,96,187],"consider":[1],"the":[2,6,15,18,28,68,71,93,117,120,152],"problem":[3,86],"of":[4,8,20,70,78,92,119,156],"fitting":[5],"parameters":[7,21],"a":[9,32,76,89,98],"high-dimensional":[10],"linear":[11,51],"regression":[12],"model.":[13],"In":[14],"regime":[16],"where":[17],"number":[19],"p":[22],"is":[23,103],"comparable":[24],"to":[25,61,174],"or":[26,65],"exceeds":[27],"sample":[29,132,168],"size":[30,133],"n,":[31],"successful":[33],"approach":[34,114],"uses":[35],"an":[36],"\u2113":[37],"<sub":[38,138,148,178],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[39,139,143,149,179,184],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[40],"-penalized":[41],"least":[42,55],"squares":[43],"estimator,":[44],"known":[45],"as":[46],"Lasso.":[47],"Unfortunately,":[48],"unlike":[49],"for":[50,106,165],"estimators":[52],"(e.g.":[53],"ordinary":[54],"squares),":[56],"no":[57],"well-established":[58],"method":[59,101,190],"exists":[60],"compute":[62],"confidence":[63],"intervals":[64],"p-values":[66],"on":[67,191],"basis":[69],"Lasso":[72,94],"estimator.":[73,95],"Very":[74],"recently,":[75],"line":[77],"work":[79,160],"[8],":[80],"[7],":[81],"[13]":[82],"has":[83],"addressed":[84],"this":[85],"by":[87],"constructing":[88],"debiased":[90],"version":[91],"propose":[97],"special":[99],"debiasing":[100],"that":[102,123],"well":[104],"suited":[105],"random":[107],"designs":[108],"with":[109,146,197],"sparse":[110],"inverse":[111],"covariance.":[112],"Our":[113],"improves":[115],"over":[116],"state":[118],"art":[121],"in":[122],"it":[124,171,196],"yields":[125],"nearly":[126],"optimal":[127],"average":[128],"testing":[129],"power":[130],"if":[131],"n":[134,173],"asymptotically":[135,175],"dominates":[136,176],"s":[137,147],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[140,150,180],"(logp)":[141],"<sup":[142,183],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[144,185],",":[145],"being":[151],"sparsity":[153],"level":[154],"(number":[155],"non-zero":[157],"coefficients).":[158],"Earlier":[159],"achieved":[161],"similar":[162],"performances":[163],"only":[164],"much":[166],"larger":[167],"size,":[169],"namely":[170],"requires":[172],"(s":[177],"log":[181],"p)":[182],".":[186],"evaluate":[188],"our":[189],"synthetic":[192],"data,":[193],"and":[194],"compare":[195],"earlier":[198],"proposals.":[199]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
