{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T03:30:08Z","timestamp":1764646208376,"version":"3.37.3"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T00:00:00Z","timestamp":1560297600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T00:00:00Z","timestamp":1560297600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501320","71471101"],"award-info":[{"award-number":["11501320","71471101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11426143"],"award-info":[{"award-number":["11426143"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2014AP008"],"award-info":[{"award-number":["ZR2014AP008"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s00180-019-00906-x","type":"journal-article","created":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T12:02:25Z","timestamp":1560340945000},"page":"203-226","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Computing the halfspace depth with multiple try algorithm and simulated annealing algorithm"],"prefix":"10.1007","volume":"35","author":[{"given":"Wei","family":"Shao","sequence":"first","affiliation":[]},{"given":"Yijun","family":"Zuo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,6,12]]},"reference":[{"key":"906_CR1","doi-asserted-by":"publisher","first-page":"1190","DOI":"10.1137\/0916069","volume":"16","author":"RH Byrd","year":"1995","unstructured":"Byrd RH, Liu P, Nocedal J, Zhu C (1995) A limited memory algorithm for bound constrained optimization. SIAM J Sci Comput 16:1190\u20131208","journal-title":"SIAM J Sci Comput"},{"key":"906_CR2","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/s11222-011-9301-9","volume":"23","author":"R Casarin","year":"2013","unstructured":"Casarin R, Craiu R, Leisen R (2013) Interacting multiple try algorithms with different proposal distributions. Stat Comput 23:185\u2013200","journal-title":"Stat Comput"},{"key":"906_CR3","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1016\/j.comgeo.2012.03.001","volume":"46","author":"D Chen","year":"2013","unstructured":"Chen D, Morin P, Wagner U (2013) Absolute approximation of Tukey depth: theory and experiments. Comput Geom 46:566\u2013573","journal-title":"Comput Geom"},{"key":"906_CR4","doi-asserted-by":"publisher","first-page":"4979","DOI":"10.1016\/j.csda.2008.04.021","volume":"52","author":"JA Cuesta-Albertos","year":"2008","unstructured":"Cuesta-Albertos JA, Nieto-Reyes A (2008) The random Tukey depth. Comput Stat Data Anal 52:4979\u20134988","journal-title":"Comput Stat Data Anal"},{"key":"906_CR5","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1007\/s10463-011-0324-y","volume":"64","author":"S Dutta","year":"2012","unstructured":"Dutta S, Ghosh AK (2012) On robust classification using projection depth. Ann Inst Stat Math 64:657\u2013676","journal-title":"Ann Inst Stat Math"},{"key":"906_CR6","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.csda.2015.12.011","volume":"98","author":"R Dyckerhoff","year":"2016","unstructured":"Dyckerhoff R, Mozharovskyi P (2016) Exact computation of the halfspace depth. Comput Stat Data Anal 98:19\u201330","journal-title":"Comput Stat Data Anal"},{"key":"906_CR7","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1109\/TPAMI.1984.4767596","volume":"6","author":"S Geman","year":"1984","unstructured":"Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6:721\u2013741","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"906_CR8","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","volume":"57","author":"WK Hastings","year":"1970","unstructured":"Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97\u2013109","journal-title":"Biometrika"},{"key":"906_CR9","doi-asserted-by":"publisher","first-page":"409","DOI":"10.6028\/jres.049.044","volume":"49","author":"MR Hestenes","year":"1952","unstructured":"Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Natl Bur Stand 49:409\u2013436","journal-title":"J Res Natl Bur Stand"},{"key":"906_CR10","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S Kirkpatrick","year":"1983","unstructured":"Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671\u2013680","journal-title":"Science"},{"key":"906_CR11","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/s00362-012-0488-4","volume":"55","author":"T Lange","year":"2014","unstructured":"Lange T, Mosler K, Mozharovskyi P (2014) Fast nonparametric classification based on data depth. Stat Pap 55:49\u201369","journal-title":"Stat Pap"},{"key":"906_CR12","volume-title":"Advanced markov chain Monte Carlo methods: learning from past samples","author":"F Liang","year":"2011","unstructured":"Liang F, Liu C, Carroll RJ (2011) Advanced markov chain Monte Carlo methods: learning from past samples. Wiley, West Sussex"},{"key":"906_CR13","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1080\/01621459.2013.872993","volume":"109","author":"F Liang","year":"2014","unstructured":"Liang F, Cheng Y, Lin G (2014) Simulated stochastic approximation annealing for global optimization with a square-root cooling schedule. J Am Stat Assoc 109:847\u2013863","journal-title":"J Am Stat Assoc"},{"key":"906_CR14","volume-title":"Monte Carlo strategies in scientific computing","author":"JS Liu","year":"2001","unstructured":"Liu JS (2001) Monte Carlo strategies in scientific computing. Springer, New York"},{"key":"906_CR15","doi-asserted-by":"publisher","first-page":"1395","DOI":"10.1007\/s00180-016-0697-8","volume":"32","author":"X Liu","year":"2017","unstructured":"Liu X (2017) Fast implementation of the Tukey depth. Comput Stat 32:1395\u20131410","journal-title":"Comput Stat"},{"key":"906_CR16","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1080\/01621459.2000.10473908","volume":"95","author":"JS Liu","year":"2000","unstructured":"Liu JS, Liang F, Wong WH (2000) The multiple-try and local optimization in Metropolis sampling. J Am Stat Assoc 95:121\u2013134","journal-title":"J Am Stat Assoc"},{"key":"906_CR17","doi-asserted-by":"publisher","first-page":"969","DOI":"10.1080\/03610918.2012.720744","volume":"43","author":"X Liu","year":"2014","unstructured":"Liu X, Zuo Y (2014) Computing halfspace depth and regression depth. Commun Stat Simul Comput 43:969\u2013985","journal-title":"Commun Stat Simul Comput"},{"issue":"5","key":"906_CR18","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1007\/s11425-016-0285-1","volume":"60","author":"X Liu","year":"2017","unstructured":"Liu X, Zuo Y, Wang Q (2017) Finite sample breakdown point of Tukey\u2019s halfspace median. Sci China Math 60(5):861\u2013874","journal-title":"Sci China Math"},{"key":"906_CR19","doi-asserted-by":"publisher","first-page":"1445","DOI":"10.1016\/j.spl.2012.04.008","volume":"82","author":"L Martino","year":"2012","unstructured":"Martino L, Olmo VPD, Read J (2012) A multi-point Metropolis scheme with generic weight functions. Stat Probab Lett 82:1445\u20131453","journal-title":"Stat Probab Lett"},{"key":"906_CR20","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1063\/1.1699114","volume":"21","author":"N Metropolis","year":"1953","unstructured":"Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087\u20131092","journal-title":"J Chem Phys"},{"key":"906_CR21","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1093\/comjnl\/7.4.308","volume":"7","author":"JA Nelder","year":"1965","unstructured":"Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308\u2013313","journal-title":"Comput J"},{"key":"906_CR22","first-page":"581","volume":"9","author":"S Pandolfi","year":"2010","unstructured":"Pandolfi S, Bartolucci F, Friel N (2010) A generalization of the multiple-try Metropolis algorithm for Bayesian estimation and model selection. J Mach Learn Res 9:581\u2013588","journal-title":"J Mach Learn Res"},{"key":"906_CR23","unstructured":"R Core Team (2016) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. \nhttps:\/\/www.R-project.org\/"},{"key":"906_CR24","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1080\/01621459.1999.10474129","volume":"94","author":"PJ Rousseeuw","year":"1999","unstructured":"Rousseeuw PJ, Hubert M (1999) Regression depth. J Am Stat Assoc 94:388\u2013402","journal-title":"J Am Stat Assoc"},{"key":"906_CR25","doi-asserted-by":"publisher","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":"906_CR26","doi-asserted-by":"publisher","DOI":"10.1515\/9781400841059","volume-title":"Nonlinear optimization","author":"A Ruszczynski","year":"2006","unstructured":"Ruszczynski A (2006) Nonlinear optimization. Princeton University Press, Princeton"},{"key":"906_CR27","first-page":"1","volume":"2018","author":"W Shao","year":"2018","unstructured":"Shao W, Guo G (2018) Multiple-try simulated annealing algorithm for global optimization. Math Probl Eng 2018:1\u201311","journal-title":"Math Probl Eng"},{"key":"906_CR28","doi-asserted-by":"publisher","first-page":"4026","DOI":"10.1016\/j.csda.2012.05.002","volume":"56","author":"W Shao","year":"2012","unstructured":"Shao W, Zuo Y (2012) Simulated annealing for higher dimensional projection depth. Comput Stat Data Anal 56:4026\u20134036","journal-title":"Comput Stat Data Anal"},{"key":"906_CR29","doi-asserted-by":"publisher","first-page":"2688","DOI":"10.1080\/00949655.2013.825960","volume":"84","author":"W Shao","year":"2014","unstructured":"Shao W, Guo G, Zhao G, Meng F (2014) Simulated annealing for the bounds of Kendall\u2019s tau and Spearman\u2019s rho. J Stat Comput Simul 84:2688\u20132699","journal-title":"J Stat Comput Simul"},{"key":"906_CR30","first-page":"523","volume":"2","author":"JW Tukey","year":"1975","unstructured":"Tukey JW (1975) Mathematrics and the picturing of data. Proc Int Cong Math 2:523\u2013531","journal-title":"Proc Int Cong Math"},{"key":"906_CR31","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1016218226","volume":"28","author":"Y Zuo","year":"2000","unstructured":"Zuo Y, 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\/content\/pdf\/10.1007\/s00180-019-00906-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00180-019-00906-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-019-00906-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,10]],"date-time":"2020-06-10T23:44:04Z","timestamp":1591832644000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00180-019-00906-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,12]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["906"],"URL":"https:\/\/doi.org\/10.1007\/s00180-019-00906-x","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"type":"print","value":"0943-4062"},{"type":"electronic","value":"1613-9658"}],"subject":[],"published":{"date-parts":[[2019,6,12]]},"assertion":[{"value":"29 April 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 June 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 June 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}