{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:49:56Z","timestamp":1759146596075},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2016,10,18]],"date-time":"2016-10-18T00:00:00Z","timestamp":1476748800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s00180-016-0697-8","type":"journal-article","created":{"date-parts":[[2016,10,18]],"date-time":"2016-10-18T03:51:14Z","timestamp":1476762674000},"page":"1395-1410","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Fast implementation of the Tukey depth"],"prefix":"10.1007","volume":"32","author":[{"given":"Xiaohui","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,10,18]]},"reference":[{"key":"697_CR1","doi-asserted-by":"crossref","first-page":"4979","DOI":"10.1016\/j.csda.2008.04.021","volume":"52","author":"J Cuesta-Albertos","year":"2008","unstructured":"Cuesta-Albertos J, Nieto-Reyes A (2008) The random Tukey depth. Comput Stat Data Anal 52:4979\u20134988","journal-title":"Comput Stat Data Anal"},{"key":"697_CR2","first-page":"1808","volume":"20","author":"DL Donoho","year":"1992","unstructured":"Donoho DL, Gasko M (1992) Breakdown properties of location estimates based on halfspace depth and projected outlyingness. Ann Stat 20:1808\u20131827","journal-title":"Ann Stat"},{"key":"697_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61568-9","volume-title":"Algorithms in combinatorial geometry","author":"H Edelsbrunner","year":"1987","unstructured":"Edelsbrunner H (1987) Algorithms in combinatorial geometry. Springer, Heidelberg"},{"key":"697_CR4","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1214\/09-AOS723","volume":"38","author":"M Hallin","year":"2010","unstructured":"Hallin M, Paindaveine D, \u0160iman M (2010) Multivariate quantiles and multiple-output regression quantiles: from \n                        $$L_{1}$$\n                        \n                            \n                                            \n                                \n                                    L\n                                    1\n                                \n                            \n                        \n                     optimization to halfspace depth. Ann Stat 38:635\u2013669","journal-title":"Ann Stat"},{"key":"697_CR5","volume-title":"Applied multivariate statistical analysis","author":"W H\u00e4rdle","year":"2007","unstructured":"H\u00e4rdle W, Simar L (2007) Applied multivariate statistical analysis. Springer, Heidelberg"},{"key":"697_CR6","unstructured":"Johnson T, Kwok I, Ng R (1998) Fast computation of 2-dimensional depth contours. In: Agrawal R, Stolorz P (eds) Proceedings of the 4th international conference on knowledge discovery and data mining. AAAI Press, New York, pp 224\u2013228"},{"key":"697_CR7","first-page":"1589","volume":"22","author":"L Kong","year":"2012","unstructured":"Kong L, Mizera I (2012) Quantile tomography: using quantiles with multivariate data. Stat Sin 22:1589\u20131610","journal-title":"Stat Sin"},{"key":"697_CR8","doi-asserted-by":"crossref","first-page":"2222","DOI":"10.1016\/j.jmva.2010.06.007","volume":"101","author":"L Kong","year":"2010","unstructured":"Kong L, Zuo Y (2010) Smooth depth contours characterize the underlying distribution. J Multivar Anal 101:2222\u20132226","journal-title":"J Multivar Anal"},{"key":"697_CR9","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1214\/aos\/1069362382","volume":"25","author":"H Koshevoy","year":"1997","unstructured":"Koshevoy H, Mosler K (1997) Zonoid trimming for multivariate distributions. Ann Stat 25:1998\u20132017","journal-title":"Ann Stat"},{"issue":"498","key":"697_CR10","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1080\/01621459.2012.688462","volume":"107","author":"J Li","year":"2012","unstructured":"Li J, Cuesta-Albertos JA, Liu RY (2012) DD-classifier: nonparametric classification procedure based on DD-plot. J Am Stat Assoc 107(498):737\u2013753","journal-title":"J Am Stat Assoc"},{"key":"697_CR11","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1080\/03610918.2012.720744","volume":"43","author":"X Liu","year":"2014","unstructured":"Liu X, Zuo Y (2014a) Computing halfspace depth and regression depth. Commun Stat-Simul Comput 43:969\u2013985","journal-title":"Commun Stat-Simul Comput"},{"issue":"1","key":"697_CR12","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s11222-012-9352-6","volume":"24","author":"X Liu","year":"2014","unstructured":"Liu X, Zuo Y (2014b) Computing projection depth and its associated estimators. Stat Comput 24(1):51\u201363","journal-title":"Stat Comput"},{"key":"697_CR13","doi-asserted-by":"crossref","unstructured":"Mosler K (2013) Depth statistics. In Robustness and Complex Data Structures. Springer, Berlin, pp 17\u201334","DOI":"10.1007\/978-3-642-35494-6_2"},{"key":"697_CR14","doi-asserted-by":"crossref","first-page":"2500","DOI":"10.1016\/j.csda.2009.01.017","volume":"53","author":"K Mosler","year":"2009","unstructured":"Mosler K, Lange T, Bazovkin P (2009) Computing zonoid trimmed regions of dimension \n                        $$d > 2$$\n                        \n                            \n                                            \n                                \n                                    d\n                                    >\n                                    2\n                                \n                            \n                        \n                    . Comput Stat Data Anal 53:2500\u20132510","journal-title":"Comput Stat Data Anal"},{"key":"697_CR15","unstructured":"Mozharovskyi P (2014) Contributions to depth-based classification and computation of the Tukey depth. PhD thesis. University of Cologne"},{"key":"697_CR16","doi-asserted-by":"crossref","first-page":"516","DOI":"10.2307\/2986073","volume":"45","author":"PJ Rousseeuw","year":"1996","unstructured":"Rousseeuw PJ, Ruts I (1996) Algorithm AS 307: bivariate location depth. J Appl Stat 45:516\u2013526","journal-title":"J Appl Stat"},{"key":"697_CR17","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1023\/A:1008945009397","volume":"8","author":"PJ Rousseeuw","year":"1998","unstructured":"Rousseeuw PJ, Struyf A (1998) Computing location depth and regression depth in higher dimensions. Stat Comput 8:193\u2013203","journal-title":"Stat Comput"},{"key":"697_CR18","doi-asserted-by":"crossref","DOI":"10.1002\/9780470644560","volume-title":"Analysis of financial time series","author":"RS Tsay","year":"2010","unstructured":"Tsay RS (2010) Analysis of financial time series, 3rd edn. Wiley, Hoboken","edition":"3"},{"key":"697_CR19","unstructured":"Tukey JW (1975) Mathematics and the picturing of data. In Proceedings of the international congress of mathematicians on canadian mathematical congress, Montreal, pp 523\u2013531"},{"key":"697_CR20","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1111\/1467-9868.00088","volume":"59","author":"A Yeh","year":"1997","unstructured":"Yeh A, Singh K (1997) Balanced confidence regions based on Tukey\u2019s depth and the bootstrap. J R Stat Soc Ser B 59:639\u2013652","journal-title":"J R Stat Soc Ser B"},{"key":"697_CR21","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1214\/aos\/1065705115","volume":"31","author":"YJ Zuo","year":"2003","unstructured":"Zuo YJ (2003) Projection based depth functions and associated medians. Ann Stat 31:1460\u20131490","journal-title":"Ann Stat"},{"key":"697_CR22","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1016218226","volume":"28","author":"YJ Zuo","year":"2000","unstructured":"Zuo YJ, Serfling R (2000) General notions of statistical depth function. Ann Stat 28:461\u2013482","journal-title":"Ann Stat"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00180-016-0697-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-016-0697-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-016-0697-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,10,14]],"date-time":"2017-10-14T05:04:31Z","timestamp":1507957471000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00180-016-0697-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,18]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["697"],"URL":"https:\/\/doi.org\/10.1007\/s00180-016-0697-8","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"value":"0943-4062","type":"print"},{"value":"1613-9658","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,18]]}}}