{"id":"https://openalex.org/W2165401931","doi":"https://doi.org/10.1017/s096354830000170x","title":"Multivariate Identities, Permutation and Bonferroni Upper Bounds","display_name":"Multivariate Identities, Permutation and Bonferroni Upper Bounds","publication_year":1995,"publication_date":"1995-12-01","ids":{"openalex":"https://openalex.org/W2165401931","doi":"https://doi.org/10.1017/s096354830000170x","mag":"2165401931"},"language":"en","primary_location":{"id":"doi:10.1017/s096354830000170x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354830000170x","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042342755","display_name":"Tuhao Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Tuhao Chen","raw_affiliation_strings":["School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087687676","display_name":"E. Seneta","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"E. Seneta","raw_affiliation_strings":["School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042342755"],"corresponding_institution_ids":["https://openalex.org/I129604602"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.2816706,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"4","issue":"4","first_page":"331","last_page":"342"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.9750000238418579,"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"}},"topics":[{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.9750000238418579,"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"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9635000228881836,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9509999752044678,"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/bonferroni-correction","display_name":"Bonferroni correction","score":0.8958427906036377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7939502000808716},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7876722812652588},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.7738527059555054},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6927828788757324},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5921003222465515},{"id":"https://openalex.org/keywords/multivariate-analysis","display_name":"Multivariate analysis","score":0.44854727387428284},{"id":"https://openalex.org/keywords/multivariate-analysis-of-variance","display_name":"Multivariate analysis of variance","score":0.4240989089012146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40469861030578613},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.36970946192741394},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07124635577201843}],"concepts":[{"id":"https://openalex.org/C127808970","wikidata":"https://www.wikidata.org/wiki/Q385989","display_name":"Bonferroni correction","level":2,"score":0.8958427906036377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7939502000808716},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7876722812652588},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7738527059555054},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6927828788757324},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5921003222465515},{"id":"https://openalex.org/C38180746","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate analysis","level":2,"score":0.44854727387428284},{"id":"https://openalex.org/C192424360","wikidata":"https://www.wikidata.org/wiki/Q929408","display_name":"Multivariate analysis of variance","level":2,"score":0.4240989089012146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40469861030578613},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.36970946192741394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07124635577201843},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s096354830000170x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354830000170x","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W91840881","https://openalex.org/W1555873097","https://openalex.org/W1973678899","https://openalex.org/W2000566002","https://openalex.org/W2028388346","https://openalex.org/W2030218600","https://openalex.org/W2076493031","https://openalex.org/W2319681555","https://openalex.org/W2333905478","https://openalex.org/W2485788213","https://openalex.org/W4229851667"],"related_works":["https://openalex.org/W4238920775","https://openalex.org/W4211087022","https://openalex.org/W1630858317","https://openalex.org/W2049286649","https://openalex.org/W2946178526","https://openalex.org/W4302373083","https://openalex.org/W2494052130","https://openalex.org/W3009106047","https://openalex.org/W2798513666","https://openalex.org/W2015759561"],"abstract_inverted_index":{"We":[0],"derive":[1],"identities":[2],"for":[3,18],"the":[4,19],"probability":[5,20],"that":[6,21,77],"at":[7,12],"least":[8,13],"a":[9,14,23,27,39,46,61],"1":[10,24,40,44],"and":[11,17,25,33,60,69,80],"2":[15,28,47],",":[16,29,43],"exactly":[22,26],"out":[30],"of":[31,78],"n":[32,42],"N":[34,49],"events":[35],"occur":[36],"(1":[37],"\u2264":[38,41,45,48],").":[50],"From":[51],"this,":[52],"we":[53],"produce":[54],"multivariate":[55,62],"permutation":[56],"hybrid":[57],"upper":[58,64],"bounds,":[59],"Bonferroni-type":[63],"bound":[65],"which":[66],"includes":[67],"Galambos":[68],"Xu's":[70],"[2]":[71],"optimal":[72],"result.":[73],"The":[74],"methodology":[75],"generalizes":[76],"Hoppe":[79],"Seneta":[81],"[3,":[82],"\u00a75].":[83],"A":[84],"numerical":[85],"example":[86],"is":[87],"given.":[88]},"counts_by_year":[{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
