{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,8]],"date-time":"2025-03-08T16:10:23Z","timestamp":1741450223984,"version":"3.38.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2011,8,1]],"date-time":"2011-08-01T00:00:00Z","timestamp":1312156800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2011,8]]},"DOI":"10.1007\/s11424-011-8216-z","type":"journal-article","created":{"date-parts":[[2011,8,13]],"date-time":"2011-08-13T04:19:19Z","timestamp":1313209159000},"page":"738-752","source":"Crossref","is-referenced-by-count":1,"title":["A nonparametric test against an umbrella alternative for stratified data"],"prefix":"10.1007","volume":"24","author":[{"given":"Yanqin","family":"Feng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinde","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoxin","family":"Zuo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,8,14]]},"reference":[{"key":"8216_CR1","first-page":"719","volume":"22","author":"N. Mantel","year":"1959","unstructured":"N. Mantel and W. Haenszel, Statistical aspects of the analysis of data from retrospective studies of disense, J. National Cancer Inst., 1959, 22: 719\u2013748.","journal-title":"J. National Cancer Inst."},{"key":"8216_CR2","doi-asserted-by":"crossref","first-page":"690","DOI":"10.2307\/2282717","volume":"58","author":"N. Mantel","year":"1963","unstructured":"N. Mantel, Chi-square tests with one degree of freedom: Extensions of the Mantel-Haenszel procedure, J. Amer. Stat. Assoc., 1963, 58: 690\u2013700.","journal-title":"J. Amer. Stat. Assoc."},{"key":"8216_CR3","doi-asserted-by":"crossref","first-page":"541","DOI":"10.2307\/2289940","volume":"84","author":"A. R. Sampson","year":"1989","unstructured":"A. R. Sampson and L. R. Whitaker, Estimation of multivariate distributions under stochastic ordering, J. Amer. Stat. Assoc., 1989, 84: 541\u2013548.","journal-title":"J. Amer. Stat. Assoc."},{"key":"8216_CR4","doi-asserted-by":"crossref","first-page":"744","DOI":"10.2307\/2290010","volume":"85","author":"T. Yanagawa","year":"1990","unstructured":"T. Yanagawa and Y. Fujii, Homogeneity test with a generalized Mantel-Haenszel estimator for 2 \u00d7 J contingency table, J. Amer. Stat. Assoc., 1990, 85: 744\u2013748.","journal-title":"J. Amer. Stat. Assoc."},{"key":"8216_CR5","doi-asserted-by":"crossref","first-page":"649","DOI":"10.2307\/2291078","volume":"90","author":"T. Yanagawa","year":"1995","unstructured":"T. Yanagawa and Y. Fujii, Projection-method Mantel-Haenszel estimator for k2 \u00d7 J tables, J. Amer. Stat. Assoc., 1995, 90: 649\u2013656.","journal-title":"J. Amer. Stat. Assoc."},{"key":"8216_CR6","first-page":"589","volume":"73","author":"D. G. Simpson","year":"1986","unstructured":"D. G. Simpson and B. H. Margolin, Recursive nonparametric testing for dose-response relationships subject to down-turns at high dose, Biometrika, 1986, 73: 589\u2013596.","journal-title":"Biometrika"},{"key":"8216_CR7","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1093\/biomet\/46.1-2.36","volume":"46","author":"H. Bartholomew","year":"1959","unstructured":"H. Bartholomew, A test of homogeneity for ordered alternative, Biometrika, 1959, 46: 36\u201348.","journal-title":"Biometrika"},{"key":"8216_CR8","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1111\/j.2517-6161.1961.tb00410.x","volume":"18","author":"D. J. Bartholomew","year":"1961","unstructured":"D. J. Bartholomew, A test of homogeneity of means under restricted alternatives, J. Roy. Stat. Assoc., Ser. B, 1961, 18: 239\u2013281.","journal-title":"J. Roy. Stat. Assoc., Ser. B"},{"key":"8216_CR9","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/0167-9473(94)90019-1","volume":"17","author":"R. Marcus","year":"1994","unstructured":"R. Marcus and A. Genizi, Simultaneous confidence intervals for umbrella contrasts of normal means, Comput. Stat. Data Anal., 1994, 17: 393\u2013407.","journal-title":"Comput. Stat. Data Anal."},{"key":"8216_CR10","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1016\/j.csda.2005.12.010","volume":"51","author":"P. Singh","year":"2006","unstructured":"P. Singh and W. Liu, A test against an umbrella ordered alternative, Comput. Stat. Data Anal., 2006, 51: 1957\u20131964.","journal-title":"Comput. Stat. Data Anal."},{"key":"8216_CR11","first-page":"13","volume":"51","author":"N. Z. Shi","year":"1989","unstructured":"N. Z. Shi, Testing for umbrella order restrictions on multinomial parameters, Sankhya, Ser. B, 1989, 51: 13\u201323.","journal-title":"Sankhya"},{"key":"8216_CR12","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/S0167-9473(98)00035-8","volume":"28","author":"A. Agresti","year":"1998","unstructured":"A. Agresti and B. A. Coull, Order-restricted inference using odds ratios for monotone trend alternatives in contingency tables, Comput. Stat. Data Anal., 1998, 28: 139\u2013155.","journal-title":"Comput. Stat. Data Anal."},{"key":"8216_CR13","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1080\/10485250802195440","volume":"20","author":"R. A. Giancristofaro","year":"2008","unstructured":"R. A. Giancristofaro and S. Bonnini, Moment-based multivariate permutation tests for ordinal categorical data, J. Nonparam. Stat., 2008, 20: 383\u2013393.","journal-title":"J. Nonparam. Stat."},{"key":"8216_CR14","doi-asserted-by":"crossref","first-page":"1676","DOI":"10.2307\/2291595","volume":"91","author":"Y. Wang","year":"1996","unstructured":"Y. Wang, A likelihood ratio test against stochastic ordering in several populations, J. Amer. Stat. Assoc., 1996, 91: 1676\u20131683.","journal-title":"J. Amer. Stat. Assoc."},{"key":"8216_CR15","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.2307\/2669854","volume":"93","author":"V. Dardanoni","year":"1998","unstructured":"V. Dardanoni and A. Forcina, A unified approach to likelihood inference on stochastic in a nonparametric context, J. Amer. Stat. Assoc., 1998, 93: 1112\u20131123.","journal-title":"J. Amer. Stat. Assoc."},{"key":"8216_CR16","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1016\/j.jspi.2006.03.003","volume":"137","author":"Y. Feng","year":"2007","unstructured":"Y. Feng and J. Wang, Likelihood ratio test against stochastic order in three way contingency tables, J. Stat. Plann. Inference, 2007, 137: 1362\u20131374.","journal-title":"J. Stat. Plann. Inference"},{"key":"8216_CR17","doi-asserted-by":"crossref","first-page":"233","DOI":"10.2307\/2532617","volume":"49","author":"Q. Yao","year":"1993","unstructured":"Q. Yao and D. Trictchler, An exact analysis of conditional independence in several 2\u00d7222 contingency tables, Biometrics, 1993, 49: 233\u2013236.","journal-title":"Biometrics"},{"key":"8216_CR18","doi-asserted-by":"crossref","first-page":"2599","DOI":"10.1002\/(SICI)1097-0258(19971130)16:22<2599::AID-SIM734>3.0.CO;2-9","volume":"16","author":"C. Chuang-Stein","year":"1997","unstructured":"C. Chuang-Stein and A. Agresti, A review of tests for detecting a monotone dpse-response relationship with ordinal response data, Stat. Med., 1997, 16: 2599\u20132618.","journal-title":"Stat. Med."},{"key":"8216_CR19","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S0378-3758(02)00243-4","volume":"107","author":"A. Agresti","year":"2002","unstructured":"A. Agresti and B. A. Coull, The analysis of contingency tables under inequality constraints, J. Stat. Plann. Inference, 2002, 107: 45\u201373.","journal-title":"J. Stat. Plann. Inference"},{"key":"8216_CR20","volume-title":"Nonlinear Programming: Theory and Algorithms","author":"M. S. Bazaraa","year":"1979","unstructured":"M. S. Bazaraa and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley, New York, 1979."},{"key":"8216_CR21","doi-asserted-by":"crossref","first-page":"49","DOI":"10.2307\/1403361","volume":"56","author":"A. Shapiro","year":"1988","unstructured":"A. Shapiro, Towards a unified theory of inequality constrained testing in multivariate analysis, Inter. Stat. Rev., 1988, 56: 49\u201362.","journal-title":"Inter. Stat. Rev."},{"key":"8216_CR22","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1093\/biomet\/50.3-4.403","volume":"50","author":"A. Kud\u00f4","year":"1963","unstructured":"A. Kud\u00f4, A multivariate analogue of the one-sided test, Biometrika, 1963, 50: 403\u2013418.","journal-title":"Biometrika"},{"key":"8216_CR23","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1214\/aoms\/1177699602","volume":"37","author":"P. N\u00fcesch","year":"1966","unstructured":"P. N\u00fcesch, On the problem of testing location in multivariate populations for restricted alternatives, Ann. Math. Stat., 1966, 37: 113\u2013119.","journal-title":"Ann. Math. Stat."},{"key":"8216_CR24","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1214\/aoms\/1177697723","volume":"40","author":"M. D. Perlman","year":"1969","unstructured":"M. D. Perlman, One-sided testing problems in multivariate analysis, Ann. Math. Stat., 1969, 40: 549\u2013567.","journal-title":"Ann. Math. Stat."},{"key":"8216_CR25","volume-title":"Asymptotic Theory of Statistical Inference","author":"B. L. S. Prakasa Rao","year":"1987","unstructured":"B. L. S. Prakasa Rao, Asymptotic Theory of Statistical Inference, Wiley, New York, 1987."},{"key":"8216_CR26","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1080\/03610920701648706","volume":"37","author":"Y. Feng","year":"2008","unstructured":"Y. Feng and J. Wang, Likelihood ratio test against simple stochastic ordering among several multinomial populations, Comm. Stat. Theory Methods, 2008, 37: 81\u201396.","journal-title":"Comm. Stat. Theory Methods"},{"key":"8216_CR27","volume-title":"Convergence of Probability Measures","author":"P. Billingsley","year":"1968","unstructured":"P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968."},{"key":"8216_CR28","doi-asserted-by":"crossref","first-page":"175","DOI":"10.2307\/2287064","volume":"76","author":"G. A. Mack","year":"1981","unstructured":"G. A. Mack and D. A. Wolfe, K-Sample rank tests for umbrella alternatives, J. Amer. Stat. Assoc., 1981, 76: 175\u2013181.","journal-title":"J. Amer. Stat. Assoc."},{"key":"8216_CR29","first-page":"225","volume":"84","author":"Y. Feng","year":"2011","unstructured":"Y. Feng, A test of conditional independence against a tree order alternative for stratified data, Utilitas Mathematica, 2011, 84: 225\u2013244.","journal-title":"Utilitas Mathematica"},{"key":"8216_CR30","volume-title":"Multivariate Permatation Test with Application to Biostatistic","author":"P. Pesarin","year":"2001","unstructured":"P. Pesarin, Multivariate Permatation Test with Application to Biostatistic, Wiley, Chichester, 2001."},{"key":"8216_CR31","doi-asserted-by":"crossref","first-page":"80","DOI":"10.2307\/3001968","volume":"1","author":"F. Wilcoxon","year":"1945","unstructured":"F. Wilcoxon, Individual comparisons by ranking method, Biometrics, 1945, 1: 80\u201383.","journal-title":"Biometrics"},{"key":"8216_CR32","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1002\/(SICI)1521-4036(200001)42:1<17::AID-BIMJ17>3.0.CO;2-U","volume":"42","author":"E. Brunner","year":"2000","unstructured":"E. Brunner and U. Munzel, The nonparametric Behrens-Fisher problem: Asymptotic theory and a small-sample approximation, Biom. J., 2000, 42: 17\u201325.","journal-title":"Biom. J."},{"key":"8216_CR33","doi-asserted-by":"crossref","first-page":"3399","DOI":"10.1080\/03610920903268865","volume":"39","author":"Y. Feng","year":"2010","unstructured":"Y. Feng and G. Zuo, A unified approach to likelihood inference on linear inequality constraints in contingency tables, Comm. Stat. Theory Methods, 2010, 39: 3399\u20133420.","journal-title":"Comm. Stat. Theory Methods"}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-011-8216-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-011-8216-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-011-8216-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,8]],"date-time":"2025-03-08T15:51:27Z","timestamp":1741449087000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-011-8216-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8]]},"references-count":33,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,8]]}},"alternative-id":["8216"],"URL":"https:\/\/doi.org\/10.1007\/s11424-011-8216-z","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"type":"print","value":"1009-6124"},{"type":"electronic","value":"1559-7067"}],"subject":[],"published":{"date-parts":[[2011,8]]}}}