{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T17:25:56Z","timestamp":1770744356217,"version":"3.49.0"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T00:00:00Z","timestamp":1560124800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T00:00:00Z","timestamp":1560124800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s11222-019-09881-1","type":"journal-article","created":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T16:02:43Z","timestamp":1560182563000},"page":"255-277","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Weighted likelihood mixture modeling and model-based clustering"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1511-1657","authenticated-orcid":false,"given":"Luca","family":"Greco","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Claudio","family":"Agostinelli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,6,10]]},"reference":[{"issue":"3","key":"9881_CR1","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/S0167-7152(01)00193-6","volume":"56","author":"C Agostinelli","year":"2002","unstructured":"Agostinelli, C.: Robust model selection in regression via weighted likelihood methodology. Stat. Probab. Lett. 56(3), 289\u2013300 (2002)","journal-title":"Stat. Probab. Lett."},{"issue":"17","key":"9881_CR2","doi-asserted-by":"publisher","first-page":"1930","DOI":"10.1016\/j.spl.2006.04.048","volume":"76","author":"C Agostinelli","year":"2006","unstructured":"Agostinelli, C.: Notes on pearson residuals and weighted likelihood estimating equations. Stat. Probab. Lett. 76(17), 1930\u20131934 (2006)","journal-title":"Stat. Probab. Lett."},{"issue":"1","key":"9881_CR3","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/s00180-011-0301-1","volume":"28","author":"C Agostinelli","year":"2013","unstructured":"Agostinelli, C., Greco, L.: A weighted strategy to handle likelihood uncertainty in Bayesian inference. Comput. Stat. 28(1), 319\u2013339 (2013)","journal-title":"Comput. Stat."},{"key":"9881_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/s10260-017-0416-9","author":"C Agostinelli","year":"2017","unstructured":"Agostinelli, C., Greco, L.: Discussion on \u201cThe power of monitoring: how to make the most of a contaminated sample\u201d. Stat. Methods Appl. (2017). https:\/\/doi.org\/10.1007\/s10260-017-0416-9","journal-title":"Stat. Methods Appl."},{"key":"9881_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/s11749-018-0596-0","author":"C Agostinelli","year":"2018","unstructured":"Agostinelli, C., Greco, L.: Weighted likelihood estimation of multivariate location and scatter. Test (2018). https:\/\/doi.org\/10.1007\/s11749-018-0596-0","journal-title":"Test"},{"key":"9881_CR6","volume-title":"Exploring Multivariate Data with the Forward Search","author":"A Atkinson","year":"2013","unstructured":"Atkinson, A., Riani, M., Cerioli, A.: Exploring Multivariate Data with the Forward Search. Springer, Berlin (2013)"},{"issue":"4","key":"9881_CR7","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1007\/BF00773476","volume":"46","author":"A Basu","year":"1994","unstructured":"Basu, A., Lindsay, B.: Minimum disparity estimation for continuous models: efficiency, distributions and robustness. Ann. Inst. Stat. Math. 46(4), 683\u2013705 (1994)","journal-title":"Ann. Inst. Stat. Math."},{"key":"9881_CR8","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.csda.2012.12.008","volume":"71","author":"C Bouveyron","year":"2014","unstructured":"Bouveyron, C., Brunet-Saumard, C.: Model-based clustering of high-dimensional data: a review. Comput. Stat. Data Anal. 71, 52\u201378 (2014)","journal-title":"Comput. Stat. Data Anal."},{"issue":"1","key":"9881_CR9","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/BF02616246","volume":"8","author":"P Bryant","year":"1991","unstructured":"Bryant, P.: Large-sample results for optimization-based clustering methods. J. Classif. 8(1), 31\u201344 (1991)","journal-title":"J. Classif."},{"issue":"5","key":"9881_CR10","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/BF01886327","volume":"16","author":"N Campbell","year":"1984","unstructured":"Campbell, N.: Mixture models and atypical values. Math. Geol. 16(5), 465\u2013477 (1984)","journal-title":"Math. Geol."},{"issue":"3\u20134","key":"9881_CR11","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1080\/00949659308811525","volume":"47","author":"G Celeux","year":"1993","unstructured":"Celeux, G., Govaert, G.: Comparison of the mixture and the classification maximum likelihood in cluster analysis. J. Stat. Comput. Simul. 47(3\u20134), 127\u2013146 (1993)","journal-title":"J. Stat. Comput. Simul."},{"issue":"489","key":"9881_CR12","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1198\/jasa.2009.tm09147","volume":"105","author":"A Cerioli","year":"2010","unstructured":"Cerioli, A.: Multivariate outlier detection with high-breakdown estimators. J. Am. Stat. Assoc. 105(489), 147\u2013156 (2010)","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"9881_CR13","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1016\/j.csda.2010.05.021","volume":"55","author":"A Cerioli","year":"2011","unstructured":"Cerioli, A., Farcomeni, A.: Error rates for multivariate outlier detection. Comput. Stat. Data Anal. 55(1), 544\u2013553 (2011)","journal-title":"Comput. Stat. Data Anal."},{"key":"9881_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/s10260-017-0409-8","author":"A Cerioli","year":"2017","unstructured":"Cerioli, A., Riani, M., Atkinson, A., Corbellini, A.: The power of monitoring: how to make the most of a contaminated sample. Stat. Methods Appl. (2017). https:\/\/doi.org\/10.1007\/s10260-017-0409-8","journal-title":"Stat. Methods Appl."},{"key":"9881_CR15","first-page":"198","volume-title":"Recognizing Family, Genus, and Species of Anuran Using a Hierarchical Classification Approach. Lecture Notes in Computer Science","author":"JG Colonna","year":"2016","unstructured":"Colonna, J.G., Gama, J., Nakamura, E.: Recognizing Family, Genus, and Species of Anuran Using a Hierarchical Classification Approach. Lecture Notes in Computer Science, pp. 198\u2013212. Springer, Berlin (2016)"},{"issue":"516","key":"9881_CR16","doi-asserted-by":"publisher","first-page":"1648","DOI":"10.1080\/01621459.2015.1100996","volume":"111","author":"P Coretto","year":"2016","unstructured":"Coretto, P., Hennig, C.: Robust improper maximum likelihood: tuning, computation, and a comparison with other methods for robust gaussian clustering. J. Am. Stat. Assoc. 111(516), 1648\u20131659 (2016)","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"9881_CR17","first-page":"5199","volume":"18","author":"P Coretto","year":"2017","unstructured":"Coretto, P., Hennig, C.: Consistency, breakdown robustness, and algorithms for robust improper maximum likelihood clustering. J. Mach. Learn. Res. 18(1), 5199\u20135237 (2017)","journal-title":"J. Mach. Learn. Res."},{"issue":"3","key":"9881_CR18","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1093\/biomet\/56.3.463","volume":"56","author":"N Day","year":"1969","unstructured":"Day, N.: Estimating the components of a mixture of normal distributions. Biometrika 56(3), 463\u2013474 (1969)","journal-title":"Biometrika"},{"key":"9881_CR19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"A Dempster","year":"1977","unstructured":"Dempster, A., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B Methodol. 39, 1\u201338 (1977)","journal-title":"J. R. Stat. Soc. Ser. B Methodol."},{"issue":"3","key":"9881_CR20","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1080\/00949655.2018.1554659","volume":"89","author":"F Dotto","year":"2019","unstructured":"Dotto, F., Farcomeni, A.: Robust inference for parsimonious model-based clustering. J. Stat. Comput. Simul. 89(3), 414\u2013442 (2019)","journal-title":"J. Stat. Comput. Simul."},{"issue":"2","key":"9881_CR21","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s11222-017-9742-x","volume":"28","author":"F Dotto","year":"2016","unstructured":"Dotto, F., Farcomeni, A., Garcia-Escudero, L.A., Mayo-Iscar, A.: A reweighting approach to robust clustering. Stat. Comput. 28(2), 477\u2013493 (2016)","journal-title":"Stat. Comput."},{"issue":"1","key":"9881_CR22","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1198\/1061860043092","volume":"13","author":"M Elashoff","year":"2004","unstructured":"Elashoff, M., Ryan, L.: An em algorithm for estimating equations. J. Comput. Graph. Stat. 13(1), 48\u201365 (2004)","journal-title":"J. Comput. Graph. Stat."},{"key":"9881_CR23","volume-title":"Robust Methods for Data Reduction","author":"A Farcomeni","year":"2015","unstructured":"Farcomeni, A., Greco, L.: Robust Methods for Data Reduction. CRC Press, Boca Raton (2015a)"},{"issue":"1","key":"9881_CR24","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s00180-014-0521-2","volume":"30","author":"A Farcomeni","year":"2015","unstructured":"Farcomeni, A., Greco, L.: S-estimation of hidden Markov models. Comput. Stat. 30(1), 57\u201380 (2015b)","journal-title":"Comput. Stat."},{"issue":"8","key":"9881_CR25","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1093\/comjnl\/41.8.578","volume":"41","author":"C Fraley","year":"1998","unstructured":"Fraley, C., Raftery, A.: How many clusters? Which clustering method? Answers via model-based cluster analysis. Comput. J. 41(8), 578\u2013588 (1998)","journal-title":"Comput. J."},{"issue":"458","key":"9881_CR26","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1198\/016214502760047131","volume":"97","author":"C Fraley","year":"2002","unstructured":"Fraley, C., Raftery, A.: Model-based clustering, discriminant analysis, and density estimation. J. Am. Stat. Assoc. 97(458), 611\u2013631 (2002)","journal-title":"J. Am. Stat. Assoc."},{"key":"9881_CR27","unstructured":"Fraley, C., Raftery, A., Murphy, T., Scrucca, L.: mclust version 4 for r: normal mixture modeling for model-based clustering, classification, and density estimation. Technical Report 597, University of Washington, Seattle (2012)"},{"key":"9881_CR28","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/j.csda.2012.11.018","volume":"61","author":"H Fritz","year":"2013","unstructured":"Fritz, H., Garcia-Escudero, L., Mayo-Iscar, A.: A fast algorithm for robust constrained clustering. Comput. Stat. Data Anal. 61, 124\u2013136 (2013)","journal-title":"Comput. Stat. Data Anal."},{"key":"9881_CR29","doi-asserted-by":"publisher","first-page":"1324","DOI":"10.1214\/07-AOS515","volume":"36","author":"L Garcia-Escudero","year":"2008","unstructured":"Garcia-Escudero, L., Gordaliza, A., Matran, C., Mayo-Iscar, A.: A general trimming approach to robust cluster analysis. Ann. Stat. 36, 1324\u20131345 (2008)","journal-title":"Ann. Stat."},{"issue":"4","key":"9881_CR30","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1007\/s11222-010-9194-z","volume":"21","author":"LA Garc\u00eda-Escudero","year":"2011","unstructured":"Garc\u00eda-Escudero, L.A., Gordaliza, A., Matr\u00e1n, C., Mayo-Iscar, A.: Exploring the number of groups in robust model-based clustering. Stat. Comput. 21(4), 585\u2013599 (2011)","journal-title":"Stat. Comput."},{"issue":"3","key":"9881_CR31","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1007\/s11222-014-9455-3","volume":"25","author":"L Garcia-Escudero","year":"2015","unstructured":"Garcia-Escudero, L., Gordaliza, A., Matran, C., Mayo-Iscar, A.: Avoiding spurious local maximizers in mixture modeling. Stat. Comput. 25(3), 619\u2013633 (2015)","journal-title":"Stat. Comput."},{"issue":"10","key":"9881_CR32","doi-asserted-by":"publisher","first-page":"7777","DOI":"10.1080\/03610918.2016.1252396","volume":"46","author":"L Greco","year":"2017","unstructured":"Greco, L.: Weighted likelihood based inference for $$p (x< y)$$. Commun. Stat. Simul. Comput. 46(10), 7777\u20137789 (2017)","journal-title":"Commun. Stat. Simul. Comput."},{"key":"9881_CR33","unstructured":"Helliwell, J., Layard, R., Sachs, J.: World Happiness Report 2018 (2018)"},{"key":"9881_CR34","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.spl.2014.08.020","volume":"96","author":"A Kuchibhotla","year":"2015","unstructured":"Kuchibhotla, A., Basu, A.: A general set up for minimum disparity estimation. Stat. Probab. Lett. 96, 68\u201374 (2015)","journal-title":"Stat. Probab. Lett."},{"key":"9881_CR35","unstructured":"Kuchibhotla, A., Basu, A.: A minimum distance weighted likelihood method of estimation. Technical report, Interdisciplinary Statistical Research Unit (ISRU), Indian Statistical Institute, Kolkata, India (2018). https:\/\/faculty.wharton.upenn.edu\/wp-content\/uploads\/2018\/02\/attemptv4p1.pdf . Accessed 17 Jan 2018"},{"issue":"2","key":"9881_CR36","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s11222-012-9362-4","volume":"24","author":"S Lee","year":"2014","unstructured":"Lee, S., McLachlan, G.: Finite mixtures of multivariate skew t-distributions: some recent and new results. Stat. Comput. 24(2), 181\u2013202 (2014)","journal-title":"Stat. Comput."},{"issue":"3","key":"9881_CR37","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/s11222-009-9128-9","volume":"20","author":"T Lin","year":"2010","unstructured":"Lin, T.: Robust mixture modeling using multivariate skew t distributions. Stat. Comput. 20(3), 343\u2013356 (2010)","journal-title":"Stat. Comput."},{"issue":"2","key":"9881_CR38","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1111\/j.0006-341X.2000.00483.x","volume":"56","author":"M Markatou","year":"2000","unstructured":"Markatou, M.: Mixture models, robustness, and the weighted likelihood methodology. Biometrics 56(2), 483\u2013486 (2000)","journal-title":"Biometrics"},{"issue":"442","key":"9881_CR39","doi-asserted-by":"publisher","first-page":"740","DOI":"10.1080\/01621459.1998.10473726","volume":"93","author":"M Markatou","year":"1998","unstructured":"Markatou, M., Basu, A., Lindsay, B.G.: Weighted likelihood equations with bootstrap root search. J. Am. Stat. Assoc. 93(442), 740\u2013750 (1998)","journal-title":"J. Am. Stat. Assoc."},{"issue":"3","key":"9881_CR40","doi-asserted-by":"publisher","first-page":"499","DOI":"10.2307\/2529203","volume":"30","author":"R Maronna","year":"1974","unstructured":"Maronna, R., Jacovkis, P.: Multivariate clustering procedures with variable metrics. Biometrics 30(3), 499\u2013505 (1974)","journal-title":"Biometrics"},{"key":"9881_CR41","volume-title":"Finite Mixture Models","author":"G McLachlan","year":"2004","unstructured":"McLachlan, G., Peel, D.: Finite Mixture Models. Wiley, New York (2004)"},{"issue":"3\u20134","key":"9881_CR42","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/S0167-9473(02)00183-4","volume":"41","author":"GJ McLachlan","year":"2003","unstructured":"McLachlan, G.J., Peel, D., Bean, R.: Modelling high-dimensional data by mixtures of factor analyzers. Comput. Stat. Data Anal. 41(3\u20134), 379\u2013388 (2003)","journal-title":"Comput. Stat. Data Anal."},{"issue":"1","key":"9881_CR43","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/j.csda.2006.12.024","volume":"52","author":"N Neykov","year":"2007","unstructured":"Neykov, N., Filzmoser, P., Dimova, R., Neytchev, P.: Robust fitting of mixtures using the trimmed likelihood estimator. Comput. Stat. Data Anal. 52(1), 299\u2013308 (2007)","journal-title":"Comput. Stat. Data Anal."},{"key":"9881_CR44","unstructured":"R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2019). https:\/\/www.R-project.org\/"},{"issue":"411","key":"9881_CR45","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1080\/01621459.1990.10474920","volume":"85","author":"P Rousseeuw","year":"1990","unstructured":"Rousseeuw, P., Van Zomeren, B.: Unmasking multivariate outliers and leverage points. J. Am. Stat. Assoc. 85(411), 633\u2013639 (1990)","journal-title":"J. Am. Stat. Assoc."},{"key":"9881_CR46","first-page":"35","volume":"77","author":"M Symon","year":"1977","unstructured":"Symon, M.: Clustering criterion and multi-variate normal mixture. Biometrics 77, 35\u201343 (1977)","journal-title":"Biometrics"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-019-09881-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-019-09881-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-019-09881-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,19]],"date-time":"2024-07-19T13:27:35Z","timestamp":1721395655000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-019-09881-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,10]]},"references-count":46,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["9881"],"URL":"https:\/\/doi.org\/10.1007\/s11222-019-09881-1","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,10]]},"assertion":[{"value":"8 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 June 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}