{"id":"https://openalex.org/W7155487196","doi":"https://doi.org/10.48550/arxiv.2604.21270","title":"CLT-Optimal Parameter Error Bounds for Linear System Identification","display_name":"CLT-Optimal Parameter Error Bounds for Linear System Identification","publication_year":2026,"publication_date":"2026-04-23","ids":{"openalex":"https://openalex.org/W7155487196","doi":"https://doi.org/10.48550/arxiv.2604.21270"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2604.21270","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2604.21270","pdf_url":"https://arxiv.org/pdf/2604.21270","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2604.21270","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134540148","display_name":"Yichen Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhou, Yichen","raw_affiliation_strings":["Department of Electrical and Computer Engineering , University of Southern Cali- fornia , Los Angeles , California , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , University of Southern Cali- fornia , Los Angeles , California , USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5127885368","display_name":"Stephen Tu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tu, Stephen","raw_affiliation_strings":["Department of Electrical and Computer Engineering , University of Southern Cali- fornia , Los Angeles , California , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , University of Southern Cali- fornia , Los Angeles , California , USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T11236","display_name":"Control Systems and Identification","score":0.9800000190734863,"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"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9800000190734863,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.007199999876320362,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.002899999963119626,"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-system-identification","display_name":"linear system identification","score":0.9340000152587891},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"central limit theorem","score":0.703000009059906},{"id":"https://openalex.org/keywords/ordinary-least-squares","display_name":"ordinary least squares","score":0.7689999938011169},{"id":"https://openalex.org/keywords/nonasymptotic-bounds","display_name":"non-asymptotic bounds","score":0.8479999899864197},{"id":"https://openalex.org/keywords/spectral-norm","display_name":"spectral norm","score":0.6700000166893005},{"id":"https://openalex.org/keywords/frobenius-norm","display_name":"Frobenius norm","score":0.9990000128746033},{"id":"https://openalex.org/keywords/stable-systems","display_name":"stable systems","score":0.7070000171661377}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7728000283241272},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5303999781608582},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4713999927043915},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.4580000042915344},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4366999864578247},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.42500001192092896},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4083999991416931},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.38179999589920044},{"id":"https://openalex.org/C2776157432","wikidata":"https://www.wikidata.org/wiki/Q1375683","display_name":"Normality","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.35190001130104065},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.334199994802475},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3328999876976013},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C79610928","wikidata":"https://www.wikidata.org/wiki/Q1656743","display_name":"Parameter identification problem","level":3,"score":0.30070000886917114},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2994000017642975},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.28610000014305115},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28349998593330383},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C179024874","wikidata":"https://www.wikidata.org/wiki/Q5395728","display_name":"Errors-in-variables models","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25609999895095825}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2604.21270","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2604.21270","pdf_url":"https://arxiv.org/pdf/2604.21270","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.2604.21270","doi":"https://doi.org/10.48550/arxiv.2604.21270","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21270","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:2604.21270","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2604.21270","pdf_url":"https://arxiv.org/pdf/2604.21270","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7155487196.pdf","grobid_xml":"https://content.openalex.org/works/W7155487196.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2903088609","https://openalex.org/W2788862106","https://openalex.org/W3082124241","https://openalex.org/W2924534955","https://openalex.org/W2762498633","https://openalex.org/W2007372876","https://openalex.org/W4411336575","https://openalex.org/W3016211582","https://openalex.org/W4313027296","https://openalex.org/W4405179146"],"abstract_inverted_index":{"There":[0],"has":[1],"been":[2],"remarkable":[3],"progress":[4],"over":[5],"the":[6,28,36,44,77,91,94,103,114,119,131,148,153],"past":[7],"decade":[8],"in":[9,43,81,161,168],"establishing":[10],"finite-sample,":[11],"non-asymptotic":[12],"bounds":[13,31,75,107,140],"on":[14],"recovering":[15],"unknown":[16],"system":[17,21,40,54],"parameters":[18],"from":[19],"observed":[20],"behavior.":[22],"Surprisingly,":[23],"however,":[24],"we":[25,62,100,127,137],"show":[26,128],"that":[27,126,151],"current":[29,74],"state-of-the-art":[30],"do":[32],"not":[33],"accurately":[34],"capture":[35],"statistical":[37],"complexity":[38],"of":[39,48,69,90,93,113],"identification,":[41],"even":[42],"most":[45],"fundamental":[46],"setting":[47,150],"estimating":[49],"a":[50,88,109,123],"discrete-time":[51],"linear":[52],"dynamical":[53],"(LDS)":[55],"via":[56,108],"ordinary":[57],"least-squares":[58],"regression":[59],"(OLS).":[60],"Specifically,":[61],"utilize":[63],"asymptotic":[64],"normality":[65],"to":[66,158],"identify":[67],"classes":[68],"problem":[70],"instances":[71],"for":[72,141],"which":[73],"overstate":[76],"squared":[78],"parameter":[79,105,115],"error,":[80,116],"both":[82,142],"spectral":[83,169],"and":[84,146,164],"Frobenius":[85,162],"norm,":[86,163],"by":[87,97],"factor":[89],"state-dimension":[92,166],"system.":[95],"Informed":[96],"this":[98],"discrepancy,":[99],"then":[101],"sharpen":[102],"OLS":[104],"error":[106],"novel":[110],"second-order":[111],"decomposition":[112],"where":[117],"crucially":[118],"lower-order":[120],"term":[121],"is":[122],"matrix-valued":[124],"martingale":[125],"correctly":[129],"captures":[130],"CLT":[132],"scaling.":[133],"From":[134],"our":[135],"analysis":[136],"obtain":[138],"finite-sample":[139],"(i)":[143],"stable":[144],"systems":[145],"(ii)":[147],"many-trajectories":[149],"match":[152],"instance-specific":[154],"optimal":[155],"rates":[156],"up":[157],"constant":[159],"factors":[160,167],"polylogarithmic":[165],"norm.":[170]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-04-25T00:00:00"}