{"id":"https://openalex.org/W7214112205","doi":"https://doi.org/10.48550/arxiv.2609.25599","title":"High-Dimensional Two-Sample Inference via Marginal Likelihood-Ratio Rank Statistics","display_name":"High-Dimensional Two-Sample Inference via Marginal Likelihood-Ratio Rank Statistics","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214112205","doi":"https://doi.org/10.48550/arxiv.2609.25599"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25599","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25599","pdf_url":"https://arxiv.org/pdf/2609.25599","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/2609.25599","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152568581","display_name":"Xiaoxu Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Xiaoxu","raw_affiliation_strings":["Nankai University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nankai University","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152540540","display_name":"Long Feng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng, Long","raw_affiliation_strings":["Nankai University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nankai University","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I205237279"],"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/T10136","display_name":"Statistical Methods and Inference","score":0.9810000061988831,"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":0.9810000061988831,"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/T11716","display_name":"Random Matrices and Applications","score":0.00559999980032444,"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":0.003800000064074993,"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/rank-based-inference","display_name":"rank-based inference","score":0.7210000157356262},{"id":"https://openalex.org/keywords/signal-sparsity","display_name":"signal sparsity","score":0.7279999852180481},{"id":"https://openalex.org/keywords/asymptotic-normality","display_name":"asymptotic normality","score":0.8050000071525574},{"id":"https://openalex.org/keywords/asymptotic-independence","display_name":"asymptotic independence","score":0.6389999985694885},{"id":"https://openalex.org/keywords/shape-change","display_name":"shape transformation","score":0.36500000953674316},{"id":"https://openalex.org/keywords/parkinson-s-disease","display_name":"Parkinson's disease","score":0.7559999823570251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7986000180244446},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.6305000185966492},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5892999768257141},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5720999836921692},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.48660001158714294},{"id":"https://openalex.org/C125918824","wikidata":"https://www.wikidata.org/wiki/Q7627920","display_name":"Studentized range","level":3,"score":0.46619999408721924},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4490000009536743},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4235999882221222},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.42250001430511475},{"id":"https://openalex.org/C91528185","wikidata":"https://www.wikidata.org/wiki/Q520952","display_name":"Maxima","level":3,"score":0.4203999936580658},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41999998688697815},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.3467000126838684},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C137610916","wikidata":"https://www.wikidata.org/wiki/Q1096862","display_name":"Gumbel distribution","level":3,"score":0.32120001316070557},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32019999623298645},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.30329999327659607},{"id":"https://openalex.org/C31388003","wikidata":"https://www.wikidata.org/wiki/Q7624548","display_name":"Strong consistency","level":3,"score":0.2953000068664551},{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C67226441","wikidata":"https://www.wikidata.org/wiki/Q1665389","display_name":"Robust statistics","level":3,"score":0.28220000863075256},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.263700008392334},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.2524000108242035},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.25599","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25599","pdf_url":"https://arxiv.org/pdf/2609.25599","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.2609.25599","doi":"https://doi.org/10.48550/arxiv.2609.25599","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25599","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:2609.25599","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25599","pdf_url":"https://arxiv.org/pdf/2609.25599","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/W7214112205.pdf","grobid_xml":"https://content.openalex.org/works/W7214112205.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2217964046","https://openalex.org/W4403995733","https://openalex.org/W7213373303"],"related_works":["https://openalex.org/W4401056208","https://openalex.org/W7137939009","https://openalex.org/W777849810","https://openalex.org/W2285488963","https://openalex.org/W2560647588","https://openalex.org/W3111233659","https://openalex.org/W7100299466","https://openalex.org/W4313504637","https://openalex.org/W2217964046","https://openalex.org/W2903831222"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,156],"rank-based":[3],"framework":[4],"for":[5,25,30,36,71,79,96],"high-dimensional":[6],"two-sample":[7],"testing":[8],"that":[9,106],"detects":[10],"marginal":[11,19,118],"distributional":[12],"differences":[13],"beyond":[14],"means":[15],"and":[16,33,46,60,76,110,119,133,141,159,169],"variances.":[17],"Three":[18],"likelihood-ratio":[20],"statistics":[21,75,83],"generate":[22],"SUM":[23,74,128,168],"tests":[24,29],"widespread":[26],"differences,":[27],"MAX":[28,82,126,170],"concentrated":[31],"departures,":[32],"Cauchy":[34,94,123],"combinations":[35,124],"unknown":[37],"signal":[38],"sparsity.":[39],"The":[40,99],"procedures":[41],"retain":[42],"all":[43],"pooled":[44],"ranks":[45],"impose":[47],"no":[48],"moment":[49],"conditions":[50],"on":[51,130],"continuous":[52],"margins.":[53],"For":[54],"unequal":[55],"but":[56],"comparable":[57],"sample":[58],"sizes":[59],"dimension":[61],"growing":[62],"polynomially":[63],"with":[64,122],"their":[65],"total,":[66],"we":[67],"establish":[68],"normal":[69],"limits":[70,78,95],"the":[72,80,97,147,164],"studentized":[73],"Gumbel":[77],"normalized":[81],"under":[84,116],"weak":[85],"Gaussian-copula":[86],"dependence.":[87],"Their":[88],"within-family":[89],"asymptotic":[90],"independence":[91],"yields":[92],"standard":[93],"combinations.":[98],"integrated":[100],"maxima":[101],"require":[102],"family-specific":[103],"centering":[104],"corrections":[105],"accommodate":[107],"interior,":[108],"critical,":[109],"boundary":[111],"regimes.":[112],"Consistency":[113],"is":[114],"established":[115],"shrinking":[117],"aggregate":[120],"signals,":[121],"retaining":[125],"or":[127],"consistency":[129],"specified":[131],"sparse":[132],"dense":[134],"alternative":[135],"classes.":[136],"Simulations":[137],"examine":[138],"location,":[139],"scale,":[140],"shape":[142],"changes,":[143],"including":[144],"alternatives":[145],"preserving":[146],"first":[148],"two":[149],"moments.":[150],"Applications":[151],"to":[152],"acoustic":[153],"measurements":[154],"from":[155],"Parkinson's":[157],"cohort":[158],"leukemia":[160],"gene-expression":[161],"data":[162],"illustrate":[163],"complementary":[165],"benefits":[166],"of":[167],"aggregation.":[171]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}