{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T14:42:56Z","timestamp":1778078576113,"version":"3.51.4"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2020,8,28]],"date-time":"2020-08-28T00:00:00Z","timestamp":1598572800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,28]],"date-time":"2020-08-28T00:00:00Z","timestamp":1598572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2020,11]]},"DOI":"10.1007\/s11222-020-09967-1","type":"journal-article","created":{"date-parts":[[2020,8,28]],"date-time":"2020-08-28T09:11:50Z","timestamp":1598605910000},"page":"1707-1723","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On some consistent tests of mutual independence among several random vectors of arbitrary dimensions"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7191-748X","authenticated-orcid":false,"given":"Angshuman","family":"Roy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0412-6826","authenticated-orcid":false,"given":"Soham","family":"Sarkar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2476-8458","authenticated-orcid":false,"given":"Anil K.","family":"Ghosh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alok","family":"Goswami","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,8,28]]},"reference":[{"key":"9967_CR1","first-page":"2518","volume":"18","author":"M Bilodeau","year":"2017","unstructured":"Bilodeau, M., Nangue, A.G.: Tests of mutual or serial independence of random vectors with applications. J. Mach. Learn. Res. 18, 2518\u20132557 (2017)","journal-title":"J. Mach. Learn. Res."},{"key":"9967_CR2","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.jspi.2016.02.007","volume":"175","author":"M Biswas","year":"2016","unstructured":"Biswas, M., Sarkar, S., Ghosh, A.K.: On some exact distribution-free tests of independence between two random vectors of arbitrary dimensions. J. Statist. Plan. Inf. 175, 78\u201386 (2016)","journal-title":"J. Statist. Plan. Inf."},{"key":"9967_CR3","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1093\/biomet\/50.1-2.81","volume":"50","author":"E Breitenberger","year":"1963","unstructured":"Breitenberger, E.: Analogues of the normal distribution on the circle and the sphere. Biometrika 50, 81\u201388 (1963)","journal-title":"Biometrika"},{"key":"9967_CR4","doi-asserted-by":"publisher","first-page":"1638","DOI":"10.1080\/01621459.2018.1513364","volume":"114","author":"S Chakraborty","year":"2019","unstructured":"Chakraborty, S., Zhang, X.: Distance metrics for measuring joint dependence with application to causal inference. J. Am. Stat. Assoc. 114, 1638\u20131650 (2019)","journal-title":"J. Am. Stat. Assoc."},{"key":"9967_CR5","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.jmva.2016.09.014","volume":"153","author":"Y Fan","year":"2017","unstructured":"Fan, Y., Lafaye de Micheaux, P., Penev, S., Salopek, D.: Multivariate nonparametric test of independence. J. Multivar. Anal. 153, 189\u2013210 (2017)","journal-title":"J. Multivar. Anal."},{"key":"9967_CR6","volume-title":"Nonparametric Functional Data Analysis: Theory and Practice","author":"F Ferraty","year":"2006","unstructured":"Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice. Springer, Berlin (2006)"},{"key":"9967_CR7","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1214\/aos\/1176346148","volume":"11","author":"JH Friedman","year":"1983","unstructured":"Friedman, J.H., Rafsky, L.C.: Graph-theoretic measures of multivariate association and prediction. Ann. Stat. 11, 377\u2013391 (1983)","journal-title":"Ann. Stat."},{"key":"9967_CR8","unstructured":"Fukumizu, K., Gretton, A., Lanckriet, G.R., Sch\u00f6lkopf, B., Sriperumbudur, B.K.: Kernel choice and classifiability for rkhs embeddings of probability distributions. Adv. Neural Inf. Process. Syst. 1750\u20131758 (2009)"},{"key":"9967_CR9","doi-asserted-by":"publisher","first-page":"2571","DOI":"10.1016\/j.jmva.2010.07.006","volume":"101","author":"S Gai\u00dfer","year":"2010","unstructured":"Gai\u00dfer, S., Ruppert, M., Schmid, F.: A multivariate version of Hoeffding\u2019s phi-square. J. Multivar. Anal. 101, 2571\u20132586 (2010)","journal-title":"J. Multivar. Anal."},{"key":"9967_CR10","doi-asserted-by":"publisher","first-page":"1592","DOI":"10.1109\/TPAMI.2005.204","volume":"27","author":"AK Ghosh","year":"2005","unstructured":"Ghosh, A.K., Chaudhuri, P., Murthy, C.: On visualization and aggregation of nearest neighbor classifiers. IEEE Trans. Pattern Anal. Mach. Intell. 27, 1592\u20131602 (2005)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"9967_CR11","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1198\/004017005000000391","volume":"48","author":"AK Ghosh","year":"2006","unstructured":"Ghosh, A.K., Chaudhuri, P., Sengupta, D.: Classification using kernel density estimates: multiscale analysis and visualization. Technometrics 48, 120\u2013132 (2006)","journal-title":"Technometrics"},{"key":"9967_CR12","first-page":"723","volume":"13","author":"A Gretton","year":"2012","unstructured":"Gretton, A., Borgwardt, K.M., Rasch, M.J., Sch\u00f6lkopf, B., Smola, A.: A kernel two-sample test. J. Mach. Learn. Res. 13, 723\u2013773 (2012)","journal-title":"J. Mach. Learn. Res."},{"key":"9967_CR13","unstructured":"Gretton, A., Fukumizu, K., Teo, C.H., Song, L., Sch\u00f6lkopf, B., Smola, A.: A kernel statistical test of independence. Adv. Neural Inf. Process. Syst. 585\u2013592 (2007)"},{"key":"9967_CR14","first-page":"1391","volume":"11","author":"A Gretton","year":"2010","unstructured":"Gretton, A., Gyorfi, L.: Consistent nonparametric tests of independence. J. Mach. Learn. Res. 11, 1391\u20131423 (2010)","journal-title":"J. Mach. Learn. Res."},{"key":"9967_CR15","doi-asserted-by":"publisher","first-page":"3097","DOI":"10.1016\/j.jspi.2012.06.003","volume":"142","author":"R Heller","year":"2012","unstructured":"Heller, R., Gorfine, M., Heller, Y.: A class of multivariate distribution-free tests of independence based on graphs. J. Stat. Plan. Inf. 142, 3097\u20133106 (2012)","journal-title":"J. Stat. Plan. Inf."},{"key":"9967_CR16","unstructured":"Heller, R., Heller, Y.: Multivariate tests of association based on univariate tests. Adv. Neural Inf. Process. Syst. 208\u2013216 (2016)"},{"key":"9967_CR17","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1093\/biomet\/ass070","volume":"100","author":"R Heller","year":"2013","unstructured":"Heller, R., Heller, Y., Gorfine, M.: A consistent multivariate test of association based on ranks of distances. Biometrika 100, 503\u2013510 (2013)","journal-title":"Biometrika"},{"key":"9967_CR18","unstructured":"Huang, C., Huo, X.: A statistically and numerically efficient independence test based on random projections and distance covariance. arXiv preprint arXiv:1701.06054 (2017)"},{"key":"9967_CR19","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1016\/j.jmva.2018.08.006","volume":"168","author":"Z Jin","year":"2018","unstructured":"Jin, Z., Matteson, D.S.: Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete v-statistics. J. Multivar. Anal. 168, 304\u2013322 (2018)","journal-title":"J. Multivar. Anal."},{"key":"9967_CR20","volume-title":"Directional Statistics","author":"KV Mardia","year":"2009","unstructured":"Mardia, K.V., Jupp, P.E.: Directional Statistics. Wiley, New Yok (2009)"},{"key":"9967_CR21","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1080\/00401706.1973.10489073","volume":"15","author":"GC McDonald","year":"1973","unstructured":"McDonald, G.C., Schwing, R.C.: Instabilities of regression estimates relating air pollution to mortality. Technometrics 15, 463\u2013481 (1973)","journal-title":"Technometrics"},{"key":"9967_CR22","doi-asserted-by":"crossref","unstructured":"Nelsen, R.B.: Nonparametric measures of multivariate association. Lecture Notes-Monograph Series 223\u2013232 (1996)","DOI":"10.1214\/lnms\/1215452621"},{"key":"9967_CR23","volume-title":"An Introduction to Copulas","author":"RB Nelsen","year":"2006","unstructured":"Nelsen, R.B.: An Introduction to Copulas. Springer, New York (2006)"},{"key":"9967_CR24","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1214\/09-AOAS34INTRO","volume":"3","author":"MA Newton","year":"2009","unstructured":"Newton, M.A.: Introducing the discussion paper by Sz\u00e9kely and Rizzo. Ann. Appl. Stat. 3, 1233\u20131235 (2009)","journal-title":"Ann. Appl. Stat."},{"key":"9967_CR25","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1111\/rssb.12235","volume":"80","author":"N Pfister","year":"2018","unstructured":"Pfister, N., B\u00fchlmann, P., Sch\u00f6lkopf, B., Peters, J.: Kernel-based tests for joint independence. J. R. Stat. Soc. Ser. B 80, 5\u201331 (2018)","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"9967_CR26","unstructured":"P\u00f3czos, B., Ghahramani, Z., Schneider, J.: Copula-based kernel dependency measures. In: Proceedings of 29th International Conference on Machine Learning, pp. 1635\u20131642 (2012)"},{"key":"9967_CR27","unstructured":"Quadrianto, N., Song, L., Smola, A.J.: Kernelized sorting. Adv. Neural Inf. Process. Syst. 1289\u20131296 (2009)"},{"key":"9967_CR28","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/BF02511160","volume":"6","author":"R Rawat","year":"2000","unstructured":"Rawat, R., Sitaram, A.: Injectivity sets for spherical means on $${\\mathbb{R}}^n$$ and on symmetric spaces. J. Fourier Anal. Appl. 6, 343\u2013348 (2000)","journal-title":"J. Fourier Anal. Appl."},{"key":"9967_CR29","doi-asserted-by":"crossref","unstructured":"Roy, A., Ghosh, A. K., Goswami, A., Murthy, C. A.: Some new copula based distribution-free tests for independence among several random variables. Sankhya, Series A. To appear (2020). https:\/\/doi.org\/10.1007\/s13171-020-00207-2","DOI":"10.1007\/s13171-020-00207-2"},{"key":"9967_CR30","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1080\/00401706.2016.1278182","volume":"60","author":"S Sarkar","year":"2018","unstructured":"Sarkar, S., Ghosh, A.K.: Some multivariate tests of independence based on ranks of nearest neighbors. Technometrics 60, 101\u2013111 (2018)","journal-title":"Technometrics"},{"key":"9967_CR31","doi-asserted-by":"publisher","first-page":"2263","DOI":"10.1214\/13-AOS1140","volume":"41","author":"D Sejdinovic","year":"2013","unstructured":"Sejdinovic, D., Sriperumbudur, B., Gretton, A., Fukumizu, K.: Equivalence of distance-based and RKHS-based statistics in hypothesis testing. Ann. Stat. 41, 2263\u20132291 (2013)","journal-title":"Ann. Stat."},{"key":"9967_CR32","doi-asserted-by":"publisher","first-page":"2769","DOI":"10.1214\/009053607000000505","volume":"35","author":"GJ Sz\u00e9kely","year":"2007","unstructured":"Sz\u00e9kely, G.J., Rizzo, M.L., Bakirov, N.K.: Measuring and testing dependence by correlation of distances. Ann. Stat. 35, 2769\u20132794 (2007)","journal-title":"Ann. Stat."},{"key":"9967_CR33","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1007\/BF02915438","volume":"57","author":"M \u00dabeda-Flores","year":"2005","unstructured":"\u00dabeda-Flores, M.: Multivariate versions of Blomqvist\u2019s beta and Spearman\u2019s footrule. Ann. Inst. Stat. Math. 57, 781\u2013788 (2005)","journal-title":"Ann. Inst. Stat. Math."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-020-09967-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-020-09967-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-020-09967-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T23:12:03Z","timestamp":1630105923000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-020-09967-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,28]]},"references-count":33,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["9967"],"URL":"https:\/\/doi.org\/10.1007\/s11222-020-09967-1","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,28]]},"assertion":[{"value":"22 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 August 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}