{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T05:01:29Z","timestamp":1782968489867,"version":"3.54.5"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[1967,7,1]],"date-time":"1967-07-01T00:00:00Z","timestamp":-79056000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1967,7,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>An unconditional non-parametric test for the bivariate two-sample problem is proposed. The test is shown to possess various desirable properties. We give critical values of the distribution, some approximations and its asymptotic distribution. For the shift type of alternative hypotheses, we show here that U is distributed asymptotically as a non-central chi-square. We have derived its Pitman's asymptotic efficiency relative to Hotelling's T \u00a02 for these alternatives and shown that in the normal case the ARE is \u00bc\u03c0. Suitable examples are constructed to show that the ARE can approach zero and infinity. An extension to the multivariate multi-sample problem is also indicated.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1967.tb00699.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T05:27:37Z","timestamp":1544160457000},"page":"320-342","source":"Crossref","is-referenced-by-count":66,"title":["A Non-Parametric Test for the Bivariate Two-Sample Location Problem"],"prefix":"10.1093","volume":"29","author":[{"given":"K. V.","family":"Mardia","sequence":"first","affiliation":[{"name":"University of Newcastle upon Tyne"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920462681700_rssb00699-cit-0001","article-title":"Some non-parametric multivariate procedures based on statistically equivalent blocks","volume-title":"Proc. Int. Symp. Multivariate Analysis","author":"Anderson","year":"1966"},{"key":"2024090920462681700_rssb00699-cit-0002","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1093\/biomet\/51.1-2.65","article-title":"Permutation support for multivariate techniques","volume":"51","author":"Arnold","year":"1964","journal-title":"Biometrika"},{"key":"2024090920462681700_rssb00699-cit-0003","first-page":"399","article-title":"On some tests of sufficient conditions leading to the normal bivariate distribution","volume":"6","author":"Bhattacharyya","year":"1943","journal-title":"Sankhy\u0101"},{"key":"2024090920462681700_rssb00699-cit-0004","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1214\/aoms\/1177700280","article-title":"On some asymptotically non-parametric competitors of Hotelling's T\n\u00a02","volume":"36","author":"Bickel","year":"1965","journal-title":"Ann. Math. Statist."},{"key":"2024090920462681700_rssb00699-cit-0005","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1080\/01621459.1958.10501451","article-title":"A new bivariate sign test","volume":"53","author":"Blumen","year":"1958","journal-title":"J. Amer. Statist. Ass."},{"key":"2024090920462681700_rssb00699-cit-0006","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1955.tb00176.x","article-title":"Permutation theory in the derivation of robust criteria and the study of departures from assumption","volume":"17","author":"Box","year":"1955","journal-title":"J. R. Statist. Soc. B"},{"key":"2024090920462681700_rssb00699-cit-0007","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1177\/0008068319640102","article-title":"Non-parametric tests for the bivariate two-sample location problem","volume":"13","author":"Chatterjee","year":"1964","journal-title":"Bull. Calcutta Statist. Ass."},{"key":"2024090920462681700_rssb00699-cit-0008","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1214\/aoms\/1177706436","article-title":"Asymptotic normality and efficiency of certain non-parametric test statistics","volume":"29","author":"Chernoff","year":"1958","journal-title":"Ann. Math. Statist."},{"key":"2024090920462681700_rssb00699-cit-0009","volume-title":"Mathematical Methods of Statistics.","author":"Cram\u00e9r","year":"1946"},{"key":"2024090920462681700_rssb00699-cit-0010","volume-title":"Non-parametric Methods in Statistics.","author":"Fraser","year":"1957"},{"key":"2024090920462681700_rssb00699-cit-0011","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1111\/j.2517-6161.1956.tb00228.x","article-title":"The asymptotic powers of certain tests based on multiple correlations","volume":"18","author":"Hannan","year":"1956","journal-title":"J. R. Statist. Soc. B"},{"key":"2024090920462681700_rssb00699-cit-0012","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1214\/aoms\/1177728498","article-title":"A bivariate sign test","volume":"26","author":"Hodges","year":"1955","journal-title":"Ann. Math. Statist."},{"key":"2024090920462681700_rssb00699-cit-0013","doi-asserted-by":"crossref","DOI":"10.2307\/3538355","volume-title":"The Advanced Theory of Statistics","author":"Kendall","year":"1961"},{"key":"2024090920462681700_rssb00699-cit-0014","volume-title":"Probability Theory","author":"Lo\u00e8ve","year":"1963","edition":"3rd ed."},{"key":"2024090920462681700_rssb00699-cit-0015","first-page":"103","article-title":"Combination in lexicographical order","volume":"6","author":"Mifsud","year":"1963","journal-title":"Comm. Ass. Computing Machinery"},{"key":"2024090920462681700_rssb00699-cit-0016","doi-asserted-by":"crossref","first-page":"119","DOI":"10.2307\/2984124","article-title":"Significance tests which may be applied to samples from any populations","volume":"4","author":"Pitman","year":"1937","journal-title":"J. R. Statist. Soc., Suppl."},{"key":"2024090920462681700_rssb00699-cit-0017","first-page":"322","article-title":"Significance tests which may be applied to samples from any populations. III: The analysis of variance test","volume":"29","author":"Pitman","year":"1938","journal-title":"Biometrika"},{"key":"2024090920462681700_rssb00699-cit-0018","first-page":"361","article-title":"Non-parametric tests for the multi-sample multivariate location problem","volume":"36","author":"Sen","year":"1965","journal-title":"Ann. Math. Statist."},{"key":"2024090920462681700_rssb00699-cit-0019","volume-title":"Sampling Theory of Surveys with Applications.","author":"Sukhatme","year":"1953"},{"key":"2024090920462681700_rssb00699-cit-0020","first-page":"1","article-title":"The limit distribution of a continuous function of random variables","volume":"35","author":"Sverdrup","year":"1952","journal-title":"Skand. Aktuar."},{"key":"2024090920462681700_rssb00699-cit-0021","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1214\/aoms\/1177699454","article-title":"Multivariate nonparametric several-sample tests","volume":"37","author":"Tamura","year":"1966","journal-title":"Ann. Math. Statist."},{"key":"2024090920462681700_rssb00699-cit-0022","volume-title":"An Introduction to Mathematical Probability.","author":"Uspensky","year":"1937"},{"key":"2024090920462681700_rssb00699-cit-0023","first-page":"695","article-title":"On two-sample tests based on order statistics","volume":"1","author":"Vincze","year":"1961","journal-title":"Proc. 4th Berkeley Symp. Math. Statist. & Probab."},{"key":"2024090920462681700_rssb00699-cit-0024","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1214\/aoms\/1177731207","article-title":"Statistical tests based on permutations of the observations","volume":"15","author":"Wald","year":"1944","journal-title":"Ann. Math. Statist."},{"key":"2024090920462681700_rssb00699-cit-0025","volume-title":"Handbook of Non-parametric Statistics","author":"Walsh","year":"1965"},{"key":"2024090920462681700_rssb00699-cit-0026","volume-title":"Mathematical Statistics","author":"Wilks","year":"1962","edition":"2nd ed."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1967.tb00699.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/29\/2\/320\/49095399\/jrsssb_29_2_320.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/29\/2\/320\/49095399\/jrsssb_29_2_320.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T20:56:02Z","timestamp":1725915362000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/29\/2\/320\/7027031"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1967,7,1]]},"references-count":26,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1967,7,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1967.tb00699.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1967,7]]},"published":{"date-parts":[[1967,7,1]]}}}