{"id":"https://openalex.org/W6967041963","doi":"https://doi.org/10.48550/arxiv.2504.02974","title":"Testing hypotheses generated by constraints","display_name":"Testing hypotheses generated by constraints","publication_year":2025,"publication_date":"2025-04-03","ids":{"openalex":"https://openalex.org/W6967041963","doi":"https://doi.org/10.48550/arxiv.2504.02974"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2504.02974","doi":"https://doi.org/10.48550/arxiv.2504.02974","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2504.02974","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2504.02974","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101961334","display_name":"Martin Larsson","orcid":"https://orcid.org/0000-0001-8219-4395","observed_orcids":["https://orcid.org/0000-0001-8219-4395"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Larsson, Martin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032389695","display_name":"Aaditya Ramdas","orcid":"https://orcid.org/0000-0003-0497-311X","observed_orcids":["https://orcid.org/0000-0003-0497-311X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ramdas, Aaditya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5064155198","display_name":"Johannes Ruf","orcid":"https://orcid.org/0000-0003-3616-2194","observed_orcids":["https://orcid.org/0000-0003-3616-2194"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ruf, Johannes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":true,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.7470999956130981,"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/T13500","display_name":"Probability and Statistical Research","score":0.7470999956130981,"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":0.08829999715089798,"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/T11235","display_name":"Statistical Methods in Clinical Trials","score":0.027499999850988388,"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/hypothesis-testing","display_name":"hypothesis testing","score":0.5740000009536743},{"id":"https://openalex.org/keywords/thresholding","display_name":"thresholding","score":0.4690000116825104},{"id":"https://openalex.org/keywords/representation-theorem","display_name":"representation theorem","score":0.781000018119812},{"id":"https://openalex.org/keywords/constraints","display_name":"constraints","score":0.35899999737739563},{"id":"https://openalex.org/keywords/sub-gaussian-distributions","display_name":"sub-Gaussian distributions","score":0.996999979019165},{"id":"https://openalex.org/keywords/group-symmetry","display_name":"group symmetry","score":0.8679999709129333},{"id":"https://openalex.org/keywords/moment-restrictions","display_name":"moment constraints","score":0.781000018119812},{"id":"https://openalex.org/keywords/conditional-value-at-risk","display_name":"conditional value at risk","score":0.9860000014305115},{"id":"https://openalex.org/keywords/expected-utility","display_name":"expected utility","score":0.699999988079071},{"id":"https://openalex.org/keywords/optimal-decision-making","display_name":"optimal decision making","score":0.7120000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7419999837875366},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.5501999855041504},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5015000104904175},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.4674000144004822},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4239000082015991},{"id":"https://openalex.org/C28901747","wikidata":"https://www.wikidata.org/wiki/Q177571","display_name":"Decision theory","level":2,"score":0.4018000066280365},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.38089999556541443},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C120577422","wikidata":"https://www.wikidata.org/wiki/Q843558","display_name":"Alternative hypothesis","level":3,"score":0.33559998869895935},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.29429998993873596},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28450000286102295},{"id":"https://openalex.org/C150325174","wikidata":"https://www.wikidata.org/wiki/Q4335500","display_name":"Optimal decision","level":3,"score":0.28279998898506165},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C178197554","wikidata":"https://www.wikidata.org/wiki/Q1099110","display_name":"Sufficient statistic","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2628999948501587},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2603999972343445},{"id":"https://openalex.org/C84839998","wikidata":"https://www.wikidata.org/wiki/Q5249245","display_name":"Decision rule","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2504.02974","doi":"https://doi.org/10.48550/arxiv.2504.02974","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2504.02974","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2504.02974","doi":"https://doi.org/10.48550/arxiv.2504.02974","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2504.02974","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.8029049634933472,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, justice, and strong institutions"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"E-variables":[0],"are":[1,145],"nonnegative":[2],"random":[3],"variables":[4],"with":[5],"expected":[6,172],"value":[7],"at":[8],"most":[9],"one":[10],"under":[11,167],"any":[12,92],"distribution":[13],"from":[14],"a":[15,43,54,66,168],"given":[16],"null":[17],"hypothesis.":[18],"Every":[19],"nonasymptotically":[20],"valid":[21],"test":[22],"can":[23],"be":[24],"obtained":[25],"by":[26,63,95,113,126],"thresholding":[27],"some":[28],"e-variable.":[29],"As":[30],"such,":[31],"e-variables":[32,90,136,166],"arise":[33],"naturally":[34],"in":[35,37,77,181,187],"applications":[36],"statistics":[38],"and":[39,42,68,123,152,162],"operations":[40],"research,":[41],"key":[44],"open":[45],"problem":[46,59],"is":[47,82],"to":[48,57,191],"characterize":[49,134],"their":[50],"form.":[51],"We":[52,102],"provide":[53],"complete":[55],"solution":[56],"this":[58,104],"for":[60,91,107,177],"hypotheses":[61,111],"generated":[62,112],"constraints":[64,148],"--":[65],"broad":[67],"natural":[69],"framework":[70],"that":[71,87],"encompasses":[72],"many":[73,115],"hypothesis":[74,93],"classes":[75],"occurring":[76],"practice.":[78],"Our":[79],"main":[80],"result":[81],"an":[83,96],"abstract":[84],"representation":[85],"theorem":[86],"describes":[88],"all":[89,135,140,184],"defined":[94],"arbitrary":[97],"collection":[98],"of":[99,164,171],"measurable":[100],"constraints.":[101],"instantiate":[103],"general":[105],"theory":[106],"three":[108],"important":[109],"classes:":[110],"finitely":[114],"constraints,":[116],"one-sided":[117],"sub-$\u03c8$":[118],"distributions":[119,124],"(including":[120],"sub-Gaussian":[121],"distributions),":[122],"constrained":[125],"group":[127],"symmetries.":[128],"In":[129],"each":[130],"case,":[131],"we":[132,159],"explicitly":[133],"as":[137,139],"well":[138],"admissible":[141],"e-variables.":[142],"Numerous":[143],"examples":[144],"treated,":[146],"including":[147],"on":[149,157],"moments,":[150],"quantiles,":[151],"conditional":[153],"value-at-risk":[154],"(CVaR).":[155],"Building":[156],"these,":[158],"prove":[160],"existence":[161],"uniqueness":[163],"optimal":[165,178],"large":[169],"class":[170],"utility-based":[173],"objective":[174],"functions":[175],"used":[176],"decision":[179],"making,":[180],"particular":[182],"covering":[183],"criteria":[185],"studied":[186],"the":[188],"e-variable":[189],"literature":[190],"date.":[192]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}
