{"id":"https://openalex.org/W7213407018","doi":"https://doi.org/10.48550/arxiv.2609.16653","title":"Marginal maximum likelihood estimation and asymptotic theory for latent variable models in high dimensions","display_name":"Marginal maximum likelihood estimation and asymptotic theory for latent variable models in high dimensions","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213407018","doi":"https://doi.org/10.48550/arxiv.2609.16653"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.16653","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16653","pdf_url":"https://arxiv.org/pdf/2609.16653","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/2609.16653","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104251740","display_name":"Chengyu Cui","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cui, Chengyu","raw_affiliation_strings":["Department of Statistics , University of Michigan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Michigan","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5151913572","display_name":"Gongjun Xu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xu, Gongjun","raw_affiliation_strings":["Department of Statistics , University of Michigan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Michigan","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27837315"],"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/T10136","display_name":"Statistical Methods and Inference","score":0.5297999978065491,"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":0.5297999978065491,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.10939999669790268,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10467","display_name":"Psychometric Methodologies and Testing","score":0.08609999716281891,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/marginal-maximum-likelihood-estimation","display_name":"marginal maximum likelihood estimation","score":0.9739999771118164},{"id":"https://openalex.org/keywords/latent-variable-modeling","display_name":"latent variable models","score":0.9629999995231628},{"id":"https://openalex.org/keywords/high-dimensional-statistics","display_name":"high-dimensional statistics","score":0.7919999957084656},{"id":"https://openalex.org/keywords/asymptotic-normality","display_name":"asymptotic normality","score":0.8870000243186951},{"id":"https://openalex.org/keywords/consistency","display_name":"consistency","score":0.9520000219345093},{"id":"https://openalex.org/keywords/marginal-likelihood","display_name":"marginal likelihood","score":0.47999998927116394},{"id":"https://openalex.org/keywords/flat-directions","display_name":"flat directions","score":0.6349999904632568},{"id":"https://openalex.org/keywords/bernstein-von-mises-theorem","display_name":"Bernstein-von Mises theorem","score":0.8669999837875366},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"uncertainty quantification","score":0.7680000066757202},{"id":"https://openalex.org/keywords/nonlinear-models","display_name":"nonlinear models","score":0.36000001430511475}],"concepts":[{"id":"https://openalex.org/C95923904","wikidata":"https://www.wikidata.org/wiki/Q6760420","display_name":"Marginal likelihood","level":3,"score":0.7418000102043152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7231000065803528},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5647000074386597},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.560699999332428},{"id":"https://openalex.org/C189559763","wikidata":"https://www.wikidata.org/wiki/Q13200161","display_name":"Likelihood principle","level":5,"score":0.5605999827384949},{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.5400999784469604},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.5388000011444092},{"id":"https://openalex.org/C119047807","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.5210000276565552},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4839000105857849},{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.4675000011920929},{"id":"https://openalex.org/C197656967","wikidata":"https://www.wikidata.org/wiki/Q17058458","display_name":"Marginal model","level":3,"score":0.45989999175071716},{"id":"https://openalex.org/C65965080","wikidata":"https://www.wikidata.org/wiki/Q1806885","display_name":"Latent variable model","level":3,"score":0.45890000462532043},{"id":"https://openalex.org/C61420037","wikidata":"https://www.wikidata.org/wiki/Q7316301","display_name":"Restricted maximum likelihood","level":3,"score":0.45089998841285706},{"id":"https://openalex.org/C191462741","wikidata":"https://www.wikidata.org/wiki/Q6795902","display_name":"Maximum likelihood sequence estimation","level":3,"score":0.4413999915122986},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4408999979496002},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.43709999322891235},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4189999997615814},{"id":"https://openalex.org/C70727504","wikidata":"https://www.wikidata.org/wiki/Q1806878","display_name":"Latent class model","level":2,"score":0.41659998893737793},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4056999981403351},{"id":"https://openalex.org/C204016326","wikidata":"https://www.wikidata.org/wiki/Q5401384","display_name":"Estimating equations","level":3,"score":0.37950000166893005},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.3792000114917755},{"id":"https://openalex.org/C89106044","wikidata":"https://www.wikidata.org/wiki/Q45284","display_name":"Likelihood function","level":3,"score":0.37389999628067017},{"id":"https://openalex.org/C143791395","wikidata":"https://www.wikidata.org/wiki/Q475208","display_name":"M-estimator","level":3,"score":0.3626999855041504},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36090001463890076},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.3467999994754791},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.3407999873161316},{"id":"https://openalex.org/C68022304","wikidata":"https://www.wikidata.org/wiki/Q842217","display_name":"Bayes estimator","level":3,"score":0.33000001311302185},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.32269999384880066},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3190999925136566},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3127000033855438},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C41587187","wikidata":"https://www.wikidata.org/wiki/Q1501882","display_name":"Generalized linear model","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C2776157432","wikidata":"https://www.wikidata.org/wiki/Q1375683","display_name":"Normality","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C156216132","wikidata":"https://www.wikidata.org/wiki/Q17099642","display_name":"Local independence","level":4,"score":0.25769999623298645},{"id":"https://openalex.org/C31388003","wikidata":"https://www.wikidata.org/wiki/Q7624548","display_name":"Strong consistency","level":3,"score":0.25450000166893005},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.16653","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16653","pdf_url":"https://arxiv.org/pdf/2609.16653","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.2609.16653","doi":"https://doi.org/10.48550/arxiv.2609.16653","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.16653","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:2609.16653","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16653","pdf_url":"https://arxiv.org/pdf/2609.16653","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/W7213407018.pdf","grobid_xml":"https://content.openalex.org/works/W7213407018.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1959608418","https://openalex.org/W3038022805","https://openalex.org/W4399695845"],"related_works":["https://openalex.org/W2129810005","https://openalex.org/W2101522492","https://openalex.org/W2166336279","https://openalex.org/W4403883602","https://openalex.org/W2801824108","https://openalex.org/W2419045928","https://openalex.org/W2185602187","https://openalex.org/W2224858857","https://openalex.org/W7095746464","https://openalex.org/W2150789748"],"abstract_inverted_index":{"This":[0],"work":[1],"addresses":[2],"a":[3,78,158,162],"longstanding":[4],"gap":[5,65],"in":[6,109,114,182],"the":[7,33,54,58,69,74,84,96,106,112,115,134,138,142,156,167],"statistical":[8],"foundations":[9,175],"of":[10,60,137,155],"marginal":[11,97,135,177],"maximum":[12,21,157],"likelihood":[13,22,98],"estimation":[14,23,178],"for":[15,47,133,166,176],"high-dimensional":[16,85,139,183],"latent":[17,29,75,143],"variable":[18,30],"models.":[19,184],"Marginal":[20],"is":[24],"widely":[25],"used":[26],"to":[27,111,127],"fit":[28],"models":[31,49],"across":[32],"social":[34],"sciences,":[35],"ecology,":[36],"and":[37,57,130,148,161,179],"machine":[38],"learning.":[39],"Despite":[40],"its":[41],"broad":[42],"use,":[43],"rigorous":[44,174],"asymptotic":[45,131,153],"theory":[46],"nonlinear":[48,79],"remains":[50],"limited":[51],"when":[52],"both":[53],"sample":[55],"size":[56],"number":[59],"observed":[61],"variables":[62,76],"diverge.":[63],"The":[64],"arises":[66],"largely":[67],"from":[68],"fact":[70],"that":[71,81,95],"integration":[72],"over":[73],"creates":[77],"objective":[80],"tightly":[82],"couples":[83],"model":[86],"parameters.":[87,140],"To":[88],"address":[89],"this":[90,120],"issue,":[91],"we":[92,123,145],"first":[93],"show":[94],"exhibits":[99],"multiple":[100],"nearly":[101],"flat":[102],"directions":[103],"even":[104],"at":[105],"true":[107],"parameter,":[108],"contrast":[110],"behavior":[113],"fixed-dimensional":[116],"case.":[117],"Building":[118],"on":[119],"geometric":[121],"characterization,":[122],"develop":[124],"new":[125],"techniques":[126],"establish":[128],"consistency":[129],"normality":[132,154],"estimator":[136,160],"For":[141],"variables,":[144],"provide":[146,173],"frequentist":[147],"Bayesian":[149],"uncertainty":[150],"quantification,":[151],"proving":[152],"posteriori":[159],"Bernstein-von":[163],"Mises-type":[164],"result":[165],"plug-in":[168],"posterior.":[169],"Together,":[170],"these":[171],"results":[172],"latent-variable":[180],"inference":[181]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-17T00:00:00"}