{"id":"https://openalex.org/W4391900853","doi":"https://doi.org/10.48550/arxiv.2402.09858","title":"An Approximation Based Theory of Linear Regression","display_name":"An Approximation Based Theory of Linear Regression","publication_year":2024,"publication_date":"2024-02-15","ids":{"openalex":"https://openalex.org/W4391900853","doi":"https://doi.org/10.48550/arxiv.2402.09858"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2402.09858","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.09858","pdf_url":"https://arxiv.org/pdf/2402.09858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2402.09858","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011191615","display_name":"Laurie Davies","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Davies, Laurie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5011191615"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.396699994802475,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.396699994802475,"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/T13141","display_name":"Statistical Methods and Applications","score":0.290800005197525,"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/T10136","display_name":"Statistical Methods and Inference","score":0.22470000386238098,"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/linear-regression","display_name":"linear regression","score":0.8840000033378601},{"id":"https://openalex.org/keywords/least-squares-approximation","display_name":"least squares approximation","score":0.8460000157356262},{"id":"https://openalex.org/keywords/high-dimensional-regression","display_name":"high-dimensional regression","score":0.7580000162124634},{"id":"https://openalex.org/keywords/vector-autoregression","display_name":"vector autoregression","score":0.9980000257492065},{"id":"https://openalex.org/keywords/john-tukey","display_name":"John Tukey","score":0.7549999952316284}],"concepts":[{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.5843371748924255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4610068202018738},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4418124854564667},{"id":"https://openalex.org/C32224588","wikidata":"https://www.wikidata.org/wiki/Q7250175","display_name":"Proper linear model","level":4,"score":0.4352790117263794},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42328575253486633},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3991013169288635},{"id":"https://openalex.org/C64946054","wikidata":"https://www.wikidata.org/wiki/Q4874476","display_name":"Bayesian multivariate linear regression","level":3,"score":0.38025742769241333},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.35027945041656494}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2402.09858","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.09858","pdf_url":"https://arxiv.org/pdf/2402.09858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2402.09858","doi":"https://doi.org/10.48550/arxiv.2402.09858","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2402.09858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2402.09858","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.09858","pdf_url":"https://arxiv.org/pdf/2402.09858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391900853.pdf","grobid_xml":"https://content.openalex.org/works/W4391900853.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3084152535","https://openalex.org/W4221144765"],"related_works":["https://openalex.org/W4226079263","https://openalex.org/W3025496867","https://openalex.org/W4221144765","https://openalex.org/W2160803212","https://openalex.org/W3084152535","https://openalex.org/W2948955561","https://openalex.org/W165709456","https://openalex.org/W3011213521","https://openalex.org/W2785013984","https://openalex.org/W2509017849"],"abstract_inverted_index":{"The":[0,73,98,145,260],"goal":[1],"of":[2,57,64,89,123,139,233,278,285],"this":[3,36,76,161,183],"paper":[4,77,151,184,261,267],"is":[5,38,52,108,118,128,135,152,165,193,199,244],"to":[6,40,48,79,93,248,274],"provide":[7],"a":[8,62,124,162,175],"theory":[9,27,86],"linear":[10,23,90],"regression":[11,24,91,221],"based":[12,26,206],"entirely":[13],"on":[14],"approximations.":[15,105],"It":[16],"will":[17,209],"be":[18,210],"argued":[19],"that":[20,35,131],"the":[21,49,55,81,85,102,121,129,143,150,169,180,186,203,228,231,283],"standard":[22,204,249],"model":[25,205],"whether":[28],"frequentist":[29],"or":[30],"Bayesian":[31],"has":[32],"failed":[33],"and":[34,70,87,92,154,222,230,241],"failure":[37],"due":[39],"an":[41,265,275],"'assumed":[42],"(revealed?)":[43],"truth'":[44],"(John":[45],"Tukey)":[46],"attitude":[47],"models.":[50],"This":[51,117,190,208,243],"reflected":[53],"in":[54,137,149,182,245,282],"language":[56],"statistical":[58],"inference":[59,280],"which":[60,127,252],"involves":[61],"concept":[63,122],"truth,":[65],"for":[66,256],"example":[67],"efficiency,":[68],"consistency":[69],"hypothesis":[71],"testing.":[72],"motivation":[74],"behind":[75],"was":[78],"remove":[80],"word":[82],"`true'":[83],"from":[84,218,224,237,264],"practice":[88],"replace":[94],"it":[95,112,198],"by":[96,179,268],"approximation.":[97],"approximations":[99,191],"considered":[100],"are":[101,172,253],"least":[103,140],"squares":[104,141],"An":[106],"approximation":[107,164],"called":[109],"valid":[110,163,254],"if":[111],"contains":[113,262],"no":[114],"irrelevant":[115],"covariates.":[116],"operationalized":[119],"using":[120,212],"Gaussian":[125,133,170,234],"P-value":[126],"probability":[130],"pure":[132],"noise":[134],"better":[136,201],"term":[138],"than":[142,174,202],"covariate.":[144],"precise":[146],"definition":[147],"given":[148],"intuitive":[153],"requires":[155],"only":[156,195,255],"four":[157,217],"simple":[158],"equations.":[159],"Given":[160],"one":[166],"where":[167],"all":[168],"P-values":[171,235,251],"less":[173],"threshold":[176],"$p0$":[177],"specified":[178],"statistician,":[181],"with":[185],"default":[187],"value":[188],"0.01.":[189],"approach":[192],"not":[194],"much":[196],"simpler":[197],"overwhelmingly":[200],"approach.":[207],"demonstrated":[211],"six":[213],"real":[214],"data":[215],"sets,":[216],"high":[219],"dimensional":[220],"two":[223],"vector":[225],"autoregression.":[226],"Both":[227],"simplicity":[229],"superiority":[232],"derive":[236],"their":[238],"universal":[239],"exactness":[240],"validity.":[242],"complete":[246],"contrast":[247],"F":[250],"carefully":[257],"designed":[258],"simulations.":[259],"excerpts":[263],"unpublished":[266],"John":[269],"Tukey":[270],"entitled":[271],"`Issues":[272],"relevant":[273],"honest":[276],"account":[277],"data-based":[279],"partially":[281],"light":[284],"Laurie":[286],"Davies's":[287],"paper'.":[288]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2024-02-18T00:00:00"}
