{"id":"https://openalex.org/W2127724926","doi":null,"title":"Thresholding Procedures for High Dimensional Variable Selection and Statistical Estimation","display_name":"Thresholding Procedures for High Dimensional Variable Selection and Statistical Estimation","publication_year":2010,"publication_date":"2010-03-13","ids":{"openalex":"https://openalex.org/W2127724926","mag":"2127724926"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.4308","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.4308","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/~szhou/threshold.pdf","raw_type":"text"},"volume":null,"type":"article","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/A5102323261","display_name":"Shuheng Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4405257864","display_name":"Seminar for Statistics","ror":"https://ror.org/05rkrf147","country_code":"CH","type":"facility","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4405257864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Shuheng Zhou","raw_affiliation_strings":["Seminar f\u00fcr Statistik, ETH, Z\u00fcrich, Switzerland#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Seminar f\u00fcr Statistik, ETH, Z\u00fcrich, Switzerland#TAB#","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4405257864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102323261"],"corresponding_institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4405257864"],"apc_list":null,"apc_paid":null,"fwci":3.8678,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.95054659,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"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":0.9994999766349792,"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":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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-variable-selection","display_name":"high-dimensional variable selection","score":0.9079999923706055},{"id":"https://openalex.org/keywords/sparse-linear-regression","display_name":"sparse linear regression","score":0.6299999952316284},{"id":"https://openalex.org/keywords/restricted-eigenvalue-condition","display_name":"restricted eigenvalue condition","score":0.8479999899864197},{"id":"https://openalex.org/keywords/model-selection-consistency","display_name":"model selection consistency","score":0.7870000004768372},{"id":"https://openalex.org/keywords/lasso","display_name":"LASSO","score":0.7070000171661377},{"id":"https://openalex.org/keywords/dantzig-selector","display_name":"Dantzig selector","score":0.8309999704360962},{"id":"https://openalex.org/keywords/sparse-vectors","display_name":"sparse vectors","score":0.4729999899864197},{"id":"https://openalex.org/keywords/mean-squared-error-bounds","display_name":"mean squared error bounds","score":0.4860000014305115}],"concepts":[{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.7616790533065796},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.7177605628967285},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6760336756706238},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6169252395629883},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5971007347106934},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.500730037689209},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4952143728733063},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.4889789819717407},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.44883981347084045},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4478507936000824},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4459545910358429},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.44396600127220154},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.4369145929813385},{"id":"https://openalex.org/C99656134","wikidata":"https://www.wikidata.org/wiki/Q2912993","display_name":"Ordinary least squares","level":2,"score":0.4290728271007538},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3445974588394165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2736268639564514},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2253367006778717},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2142733335494995},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2004586160182953},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08970829844474792},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.4308","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.4308","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/~szhou/threshold.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.841.7222","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.841.7222","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://papers.nips.cc/paper/3697-thresholding-procedures-for-high-dimensional-variable-selection-and-statistical-estimation.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W403935824","https://openalex.org/W1669557330","https://openalex.org/W1984305442","https://openalex.org/W1986931325","https://openalex.org/W2005838333","https://openalex.org/W2010824638","https://openalex.org/W2020925091","https://openalex.org/W2030449718","https://openalex.org/W2063978378","https://openalex.org/W2071168995","https://openalex.org/W2095978736","https://openalex.org/W2109842006","https://openalex.org/W2116581043","https://openalex.org/W2127300249","https://openalex.org/W2129131372","https://openalex.org/W2135046866","https://openalex.org/W2142246398","https://openalex.org/W2150940164","https://openalex.org/W2158940042","https://openalex.org/W2164452299","https://openalex.org/W2289917018","https://openalex.org/W3103643510"],"related_works":["https://openalex.org/W7099690715","https://openalex.org/W4417103366","https://openalex.org/W1486249389","https://openalex.org/W7099760248","https://openalex.org/W7097205836","https://openalex.org/W212980374","https://openalex.org/W2034260606","https://openalex.org/W2137421981","https://openalex.org/W2298319861","https://openalex.org/W4416344572"],"abstract_inverted_index":{"Given":[0],"n":[1,8],"noisy":[2],"samples":[3],"with":[4,131],"p":[5],"dimensions,":[6],"where":[7,83],"\u226a":[9],"p,":[10],"we":[11,91],"show":[12,92],"that":[13,93],"the":[14,32,68,74,84,103,109,115,123,148],"multi-step":[15],"thresholding":[16],"procedure":[17],"can":[18],"accurately":[19],"estimate":[20],"a":[21,28,97,119,153],"sparse":[22,155],"vector":[23],"\u03b2":[24],"\u2208":[25],"Rp":[26],"in":[27,53,73],"linear":[29],"model,":[30],"under":[31],"restricted":[33],"eigenvalue":[34],"conditions":[35,40],"(Bickel-Ritov-Tsybakov":[36],"09).":[37],"Thus":[38],"our":[39],"for":[41,81],"model":[42],"selection":[43],"consistency":[44],"are":[45,142,146],"considerably":[46],"weaker":[47],"than":[48],"what":[49],"has":[50],"been":[51],"achieved":[52],"previous":[54],"works.":[55],"More":[56],"importantly,":[57],"this":[58],"method":[59],"al-lows":[60],"very":[61],"significant":[62],"values":[63],"of":[64,70,122],"s,":[65],"which":[66,134,140,145],"is":[67,106],"number":[69],"non-zero":[71,143],"elements":[72],"true":[75,104],"parameter.":[76],"For":[77],"example,":[78],"it":[79],"works":[80],"cases":[82],"ordinary":[85],"Lasso":[86],"would":[87,129,135],"have":[88],"failed.":[89],"Finally,":[90],"if":[94,102],"X":[95],"obeys":[96],"uniform":[98],"uncertainty":[99],"principle":[100],"and":[101,144],"parameter":[105],"sufficiently":[107,154],"sparse,":[108],"Gauss-Dantzig":[110],"selector":[111],"(Cande\u0300s-Tao":[112],"07)":[113],"achieves":[114],"\u21132":[116],"loss":[117],"within":[118],"logarithmic":[120],"factor":[121],"ideal":[124],"mean":[125],"square":[126],"error":[127],"one":[128],"achieve":[130],"an":[132],"oracle":[133],"supply":[136],"perfect":[137],"information":[138],"about":[139],"coordinates":[141],"above":[147],"noise":[149],"level,":[150],"while":[151],"selecting":[152],"model.":[156],"1":[157]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
