{"id":"https://openalex.org/W7220748312","doi":"https://doi.org/10.48550/arxiv.2610.04069","title":"Mean squared error reduction of (plug-in) look-ahead estimators for Markov chains","display_name":"Mean squared error reduction of (plug-in) look-ahead estimators for Markov chains","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220748312","doi":"https://doi.org/10.48550/arxiv.2610.04069"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04069","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04069","pdf_url":"https://arxiv.org/pdf/2610.04069","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"},"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/2610.04069","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011241328","display_name":"Romain Aza\u00efs","orcid":"https://orcid.org/0000-0002-5234-1822","observed_orcids":["https://orcid.org/0000-0002-5234-1822"]},"institutions":[{"id":"https://openalex.org/I4394709170","display_name":"Centre Inria de Lyon","ror":"https://ror.org/022gakr41","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4394709170"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Aza\u00efs, Romain","raw_affiliation_strings":["Inria Lyon , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria Lyon , France","institution_ids":["https://openalex.org/I4394709170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110681239","display_name":"Beno\u00eet Henry","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I4210145948","display_name":"Laboratoire Paul Painlev\u00e9","ror":"https://ror.org/043n4fm24","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2279609970","https://openalex.org/I4210141950","https://openalex.org/I4210145948"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Henry, Beno\u00eet","raw_affiliation_strings":["Univ. Lille , CNRS , IMT Nord Europe , Inria , UMR 8524 -Laboratoire Paul Painlev\u00e9 , F-59000 Lille , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Lille , CNRS , IMT Nord Europe , Inria , UMR 8524 -Laboratoire Paul Painlev\u00e9 , F-59000 Lille , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2279609970","https://openalex.org/I4210145948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157788137","display_name":"Henri P\u00e9choux","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4394709170","display_name":"Centre Inria de Lyon","ror":"https://ror.org/022gakr41","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4394709170"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"P\u00e9choux, Henri","raw_affiliation_strings":["Inria Lyon , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria Lyon , France","institution_ids":["https://openalex.org/I4394709170"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","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/T12056","display_name":"Markov Chains and Monte Carlo Methods","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/T13500","display_name":"Probability and Statistical Research","score":9.999999747378752e-05,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/plug-in-estimator","display_name":"plug-in estimator","score":0.8209999799728394},{"id":"https://openalex.org/keywords/markov-chains","display_name":"Markov chains","score":0.8379999995231628},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"mean squared error","score":0.8370000123977661},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.8569999933242798},{"id":"https://openalex.org/keywords/geographic-mobility","display_name":"spatial mobility","score":0.6759999990463257},{"id":"https://openalex.org/keywords/lyon-metropolitan-area","display_name":"Lyon metropolitan area","score":0.6909999847412109}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7717999815940857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7703999876976013},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6276999711990356},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5760999917984009},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.5231000185012817},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5210999846458435},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.4609000086784363},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.439300000667572},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4056999981403351},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.40230000019073486},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C27406209","wikidata":"https://www.wikidata.org/wiki/Q6394203","display_name":"Kernel smoother","level":5,"score":0.38580000400543213},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3582000136375427},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3481000065803528},{"id":"https://openalex.org/C98385598","wikidata":"https://www.wikidata.org/wiki/Q1339385","display_name":"Empirical distribution function","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.33649998903274536},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.3314000070095062},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.3285999894142151},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.3127000033855438},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.2919999957084656},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.2775999903678894},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04069","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04069","pdf_url":"https://arxiv.org/pdf/2610.04069","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.2610.04069","doi":"https://doi.org/10.48550/arxiv.2610.04069","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04069","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:2610.04069","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04069","pdf_url":"https://arxiv.org/pdf/2610.04069","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220748312.pdf","grobid_xml":"https://content.openalex.org/works/W7220748312.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2149008764","https://openalex.org/W1983632287","https://openalex.org/W1999363529","https://openalex.org/W95892588","https://openalex.org/W1576925720","https://openalex.org/W91634276","https://openalex.org/W2089896165","https://openalex.org/W2038983037","https://openalex.org/W7074626829","https://openalex.org/W4387705873"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,5,20,32,41,44,48,56,59,78,97,103,109,128,132,149,157,162,174,179,197,200,218],"estimation":[3],"of":[4,9,19,24,43,55,77,199],"invariant":[6],"distribution":[7],"$\u03c0$":[8],"a":[10,14,25,136,167],"Markov":[11,65],"kernel":[12,45,60,133],"on":[13,102,196],"discrete":[15],"state":[16],"space":[17],"(or":[18],"mean":[21,72],"value":[22],"$\u03c0(f)$":[23],"functional":[26],"$f$":[27],"under":[28,172],"$\u03c0$)":[29],"when":[30],"solving":[31],"invariance":[33],"equation":[34],"is":[35,61,159],"not":[36],"feasible.":[37],"Look-ahead":[38],"estimators":[39,201],"exploit":[40],"knowledge":[42],"by":[46,187],"propagating":[47],"empirical":[49,79,104,180],"occupation":[50],"measure":[51],"through":[52],"$k$":[53,113],"steps":[54],"chain.":[57],"When":[58,156],"known,":[62],"as":[63],"in":[64,217],"chain":[66],"Monte":[67],"Carlo,":[68],"we":[69,142,165],"compare":[70],"their":[71],"squared":[73],"error":[74],"with":[75,112,139,152],"that":[76,108,121],"estimator,":[80],"for":[81,94,114],"independent":[82],"or":[83,87],"Markovian":[84,95],"data,":[85,96],"stationary":[86],"not.":[88],"Our":[89],"main":[90],"result":[91],"establishes":[92],"that,":[93],"one-step":[98],"estimator":[99,177],"always":[100],"improves":[101],"one":[105],"asymptotically,":[106],"and":[107,169],"improvement":[110],"grows":[111],"reversible":[115],"kernels.":[116],"A":[117],"non-reversible":[118],"counterexample":[119],"shows":[120],"reversibility":[122],"cannot":[123],"simply":[124],"be":[125],"dropped.":[126],"In":[127],"statistical":[129],"setting":[130],"where":[131],"belongs":[134],"to":[135,209],"parametric":[137,163],"family":[138],"unknown":[140],"parameter,":[141],"introduce":[143],"plug-in":[144,175],"look-ahead":[145,150,176],"estimators,":[146],"which":[147,173,191],"perform":[148],"step":[151],"an":[153],"estimated":[154,160],"kernel.":[155],"parameter":[158],"at":[161,202],"rate,":[164],"give":[166],"necessary":[168],"sufficient":[170],"condition":[171],"outperforms":[178],"one.":[181],"The":[182],"theoretical":[183],"results":[184],"are":[185,206],"illustrated":[186],"extensive":[188],"simulation":[189],"studies,":[190],"also":[192],"shed":[193],"further":[194],"light":[195],"behaviour":[198],"hand.":[203],"Both":[204],"settings":[205],"finally":[207],"applied":[208],"real":[210],"data":[211],"arising":[212],"from":[213],"geographical":[214],"mobility":[215],"problems":[216],"Lyon":[219],"metropolitan":[220],"area,":[221],"France.":[222]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-07T00:00:00"}
