{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,19]],"date-time":"2026-04-19T08:52:32Z","timestamp":1776588752968,"version":"3.51.2"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,5,13]],"date-time":"2022-05-13T00:00:00Z","timestamp":1652400000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,5,13]],"date-time":"2022-05-13T00:00:00Z","timestamp":1652400000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100008273","name":"Novartis Foundation","doi-asserted-by":"publisher","award":["FreeNovation 2019"],"award-info":[{"award-number":["FreeNovation 2019"]}],"id":[{"id":"10.13039\/100008273","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["786461"],"award-info":[{"award-number":["786461"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Prediction models often fail if train and test data do not stem from the same distribution. Out-of-distribution (OOD) generalization to unseen, perturbed test data is a desirable but difficult-to-achieve property for prediction models and in general requires strong assumptions on the data generating process (DGP). In a causally inspired perspective on OOD generalization, the test data arise from a specific class of interventions on exogenous random variables of the DGP, called anchors. Anchor regression models, introduced by Rothenh\u00e4usler et al. (J R Stat Soc Ser B 83(2):215\u2013246, 2021.<jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"doi\" xlink:href=\"https:\/\/doi.org\/10.1111\/rssb.12398\">10.1111\/rssb.12398<\/jats:ext-link>), protect against distributional shifts in the test data by employing causal regularization. However, so far anchor regression has only been used with a squared-error loss which is inapplicable to common responses such as censored continuous or ordinal data. Here, we propose a distributional version of anchor regression which generalizes the method to potentially censored responses with at least an ordered sample space. To this end, we combine a flexible class of parametric transformation models for distributional regression with an appropriate causal regularizer under a more general notion of residuals. In an exemplary application and several simulation scenarios we demonstrate the extent to which OOD generalization is possible.<\/jats:p>","DOI":"10.1007\/s11222-022-10097-z","type":"journal-article","created":{"date-parts":[[2022,5,13]],"date-time":"2022-05-13T14:03:51Z","timestamp":1652450631000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Distributional anchor regression"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7546-7356","authenticated-orcid":false,"given":"Lucas","family":"Kook","sequence":"first","affiliation":[]},{"given":"Beate","family":"Sick","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1782-6015","authenticated-orcid":false,"given":"Peter","family":"B\u00fchlmann","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,13]]},"reference":[{"key":"10097_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68560-1","volume-title":"Survival and Event History Analysis: A Process Point of View","author":"O Aalen","year":"2008","unstructured":"Aalen, O., Borgan, O., Gjessing, H.: Survival and Event History Analysis: A Process Point of View. Springer, Berlin (2008)"},{"key":"10097_CR2","unstructured":"Abadi, M. et\u00a0al.: TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. https:\/\/tensorflow.org\/, software available from tensorflow.org (2015)"},{"issue":"434","key":"10097_CR3","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1080\/01621459.1996.10476902","volume":"91","author":"JD Angrist","year":"1996","unstructured":"Angrist, J.D., Imbens, G.W., Rubin, D.B.: Identification of causal effects using instrumental variables. J. Am. Stat. Assoc. 91(434), 444\u2013455 (1996). https:\/\/doi.org\/10.1080\/01621459.1996.10476902","journal-title":"J. Am. Stat. Assoc."},{"key":"10097_CR4","unstructured":"Arjovsky, M., Bottou, L., Gulrajani, I., Lopez-Paz, D.: Invariant risk minimization. arXiv preprint arXiv:1907.02893 (2019)"},{"issue":"3","key":"10097_CR5","doi-asserted-by":"publisher","first-page":"357","DOI":"10.2307\/2347385","volume":"39","author":"A Azzalini","year":"1990","unstructured":"Azzalini, A., Bowman, A.W.: A look at some data on the old faithful Geyser. Appl. Stat. 39(3), 357 (1990). https:\/\/doi.org\/10.2307\/2347385","journal-title":"Appl. Stat."},{"issue":"1","key":"10097_CR6","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1093\/biomet\/75.1.65","volume":"75","author":"WE Barlow","year":"1988","unstructured":"Barlow, W.E., Prentice, R.L.: Residuals for relative risk regression. Biometrika 75(1), 65\u201374 (1988). https:\/\/doi.org\/10.1093\/biomet\/75.1.65","journal-title":"Biometrika"},{"key":"10097_CR7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004). https:\/\/doi.org\/10.1017\/CBO9780511804441"},{"issue":"3","key":"10097_CR8","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1214\/19-STS721","volume":"35","author":"P B\u00fchlmann","year":"2020","unstructured":"B\u00fchlmann, P.: Invariance, causality and robustness. Stat. Sci. 35(3), 404\u2013426 (2020). https:\/\/doi.org\/10.1214\/19-STS721","journal-title":"Stat. Sci."},{"issue":"1","key":"10097_CR9","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1111\/insr.12426","volume":"88","author":"P B\u00fchlmann","year":"2020","unstructured":"B\u00fchlmann, P., \u0106evid, D.: Deconfounding and causal regularisation for stability and external validity. Int. Stat. Rev. 88(1), 114\u2013134 (2020). https:\/\/doi.org\/10.1111\/insr.12426","journal-title":"Int. Stat. Rev."},{"issue":"1","key":"10097_CR10","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1023\/A:1007379606734","volume":"28","author":"R Caruana","year":"1997","unstructured":"Caruana, R.: Multitask learning. Mach. Learn. 28(1), 41\u201375 (1997). https:\/\/doi.org\/10.1023\/A:1007379606734","journal-title":"Mach. Learn."},{"issue":"261","key":"10097_CR11","first-page":"1","volume":"22","author":"Y Chen","year":"2021","unstructured":"Chen, Y., B\u00fchlmann, P.: Domain adaptation under structural causal models. J. Mach. Learn. Res. 22(261), 1\u201380 (2021)","journal-title":"J. Mach. Learn. Res."},{"key":"10097_CR12","doi-asserted-by":"publisher","DOI":"10.1109\/tpami.2021.3094760","author":"R Christiansen","year":"2021","unstructured":"Christiansen, R., Pfister, N., Jakobsen, M.E., Gnecco, N., Peters, J.: A causal framework for distribution generalization. IEEE Trans. Pattern Anal. Mach. Intell. (2021). https:\/\/doi.org\/10.1109\/tpami.2021.3094760","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"2","key":"10097_CR13","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","volume":"34","author":"DR Cox","year":"1972","unstructured":"Cox, D.R.: Regression models and life-tables. J. R. Stat. Soc. Ser. B (Methodol.) 34(2), 187\u2013202 (1972). https:\/\/doi.org\/10.1111\/j.2517-6161.1972.tb00899.x","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"issue":"2","key":"10097_CR14","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1093\/biomet\/62.2.269","volume":"62","author":"DR Cox","year":"1975","unstructured":"Cox, D.R.: Partial likelihood. Biometrika 62(2), 269\u2013276 (1975). https:\/\/doi.org\/10.1093\/biomet\/62.2.269","journal-title":"Biometrika"},{"issue":"2","key":"10097_CR15","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1111\/j.2517-6161.1968.tb00724.x","volume":"30","author":"DR Cox","year":"1968","unstructured":"Cox, D.R., Snell, E.J.: A general definition of residuals. J. R. Stat. Soc. Ser. B (Methodol.) 30(2), 248\u2013265 (1968). https:\/\/doi.org\/10.1111\/j.2517-6161.1968.tb00724.x","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"issue":"530","key":"10097_CR16","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1080\/01621459.2020.1762613","volume":"115","author":"B Efron","year":"2020","unstructured":"Efron, B.: Prediction, estimation, and attribution. J. Am. Stat. Assoc. 115(530), 636\u2013655 (2020). https:\/\/doi.org\/10.1080\/01621459.2020.1762613","journal-title":"J. Am. Stat. Assoc."},{"key":"10097_CR17","volume-title":"Regression","author":"L Fahrmeir","year":"2007","unstructured":"Fahrmeir, L., Kneib, T., Lang, S., Marx, B.: Regression. Springer, Berlin (2007)"},{"issue":"2","key":"10097_CR18","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1111\/j.0006-341X.2000.00473.x","volume":"56","author":"CP Farrington","year":"2000","unstructured":"Farrington, C.P.: Residuals for proportional hazards models with interval-censored survival data. Biometrics 56(2), 473\u2013482 (2000). https:\/\/doi.org\/10.1111\/j.0006-341X.2000.00473.x","journal-title":"Biometrics"},{"issue":"4","key":"10097_CR19","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1006\/ssre.1997.0606","volume":"26","author":"EM Foster","year":"1997","unstructured":"Foster, E.M.: Instrumental variables for logistic regression: an illustration. Soc. Sci. Res. 26(4), 487\u2013504 (1997). https:\/\/doi.org\/10.1006\/ssre.1997.0606","journal-title":"Soc. Sci. Res."},{"key":"10097_CR20","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v094.i14","author":"A Fu","year":"2020","unstructured":"Fu, A., Narasimhan, B., Boyd, S.: CVXR: an R package for disciplined convex optimization. J. Stat. Softw. (2020). https:\/\/doi.org\/10.18637\/jss.v094.i14","journal-title":"J. Stat. Softw."},{"issue":"3","key":"10097_CR21","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1006\/jeem.1996.0052","volume":"31","author":"OW Gilley","year":"1996","unstructured":"Gilley, O.W., Kelley Pace, R.: On the Harrison and rubinfeld data. J. Environ. Econ. Manag. 31(3), 403\u2013405 (1996). https:\/\/doi.org\/10.1006\/jeem.1996.0052","journal-title":"J. Environ. Econ. Manag."},{"issue":"477","key":"10097_CR22","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1198\/016214506000001437","volume":"102","author":"T Gneiting","year":"2007","unstructured":"Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc. 102(477), 359\u2013378 (2007). https:\/\/doi.org\/10.1198\/016214506000001437","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"10097_CR23","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1111\/j.2517-6161.1952.tb00104.x","volume":"14","author":"IJ Good","year":"1952","unstructured":"Good, I.J.: Rational decisions. J. Roy. Stat. Soc.: Ser. B (Methodol.) 14(1), 107\u2013114 (1952). https:\/\/doi.org\/10.1111\/j.2517-6161.1952.tb00104.x","journal-title":"J. Roy. Stat. Soc.: Ser. B (Methodol.)"},{"issue":"1","key":"10097_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/1905714","volume":"11","author":"T Haavelmo","year":"1943","unstructured":"Haavelmo, T.: The statistical implications of a system of simultaneous equations. Econometrica 11(1), 1 (1943). https:\/\/doi.org\/10.2307\/1905714","journal-title":"Econometrica"},{"issue":"1","key":"10097_CR25","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0095-0696(78)90006-2","volume":"5","author":"D Harrison","year":"1978","unstructured":"Harrison, D., Rubinfeld, D.L.: Hedonic housing prices and the demand for clean air. J. Environ. Econ. Manag. 5(1), 81\u2013102 (1978). https:\/\/doi.org\/10.1016\/0095-0696(78)90006-2","journal-title":"J. Environ. Econ. Manag."},{"key":"10097_CR26","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v092.i01","author":"T Hothorn","year":"2020","unstructured":"Hothorn, T.: Most likely transformations: the mlt package. J. Stat. Softw. (2020). https:\/\/doi.org\/10.18637\/jss.v092.i01","journal-title":"J. Stat. Softw."},{"issue":"1","key":"10097_CR27","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1111\/rssb.12017","volume":"76","author":"T Hothorn","year":"2014","unstructured":"Hothorn, T., Kneib, T., B\u00fchlmann, P.: Conditional transformation models. J. R. Stat. Soc. Ser. B Stat. Methodol. 76(1), 3\u201327 (2014). https:\/\/doi.org\/10.1111\/rssb.12017","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"issue":"1","key":"10097_CR28","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1111\/sjos.12291","volume":"45","author":"T Hothorn","year":"2018","unstructured":"Hothorn, T., M\u00f6st, L., B\u00fchlmann, P.: Most likely transformations. Scand. J. Stat. 45(1), 110\u2013134 (2018). https:\/\/doi.org\/10.1111\/sjos.12291","journal-title":"Scand. J. Stat."},{"issue":"1","key":"10097_CR29","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1111\/j.1467-985X.2004.00339.x","volume":"168","author":"GW Imbens","year":"2005","unstructured":"Imbens, G.W., Rosenbaum, P.R.: Robust, accurate confidence intervals with a weak instrument: quarter of birth and education. J. R. Stat. Soc. A. Stat. Soc. 168(1), 109\u2013126 (2005). https:\/\/doi.org\/10.1111\/j.1467-985X.2004.00339.x","journal-title":"J. R. Stat. Soc. A. Stat. Soc."},{"key":"10097_CR30","unstructured":"Kingma, D.P., Ba, J.L.: Adam: a method for stochastic optimization. In: 3rd international conference on learning representations, ICLR 2015\u2014conference track proceedings, international conference on learning representations, ICLR, https:\/\/arxiv.org\/abs\/1412.6980v9 (2015)"},{"issue":"1","key":"10097_CR31","doi-asserted-by":"publisher","first-page":"581","DOI":"10.32614\/RJ-2021-054","volume":"13","author":"L Kook","year":"2021","unstructured":"Kook, L., Hothorn, T.: Regularized transformation models: the Tramnet package. R J. 13(1), 581\u2013594 (2021). https:\/\/doi.org\/10.32614\/RJ-2021-054","journal-title":"R J."},{"key":"10097_CR32","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2021.108263","volume":"122","author":"L Kook","year":"2022","unstructured":"Kook, L., Herzog, L., Hothorn, T., D\u00fcrr, O., Sick, B.: Deep and interpretable regression models for ordinal outcomes. Pattern Recogn. 122, 108263 (2022). https:\/\/doi.org\/10.1016\/j.patcog.2021.108263","journal-title":"Pattern Recogn."},{"issue":"1","key":"10097_CR33","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1093\/biomet\/68.1.93","volume":"68","author":"SW Lagakos","year":"1981","unstructured":"Lagakos, S.W.: The graphical evaluation of explanatory variables in proportional hazard regression models. Biometrika 68(1), 93\u201398 (1981). https:\/\/doi.org\/10.1093\/biomet\/68.1.93","journal-title":"Biometrika"},{"key":"10097_CR34","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198523598.001.0001","volume-title":"Parametric Statistical Inference","author":"JK Lindsey","year":"1996","unstructured":"Lindsey, J.K., et al.: Parametric Statistical Inference. Oxford University Press, Oxford (1996)"},{"key":"10097_CR35","doi-asserted-by":"publisher","first-page":"1933","DOI":"10.12688\/f1000research.12934.1","volume":"6","author":"T Lohse","year":"2017","unstructured":"Lohse, T., Rohrmann, S., Faeh, D., Hothorn, T.: Continuous outcome logistic regression for analyzing body mass index distributions. F1000 Res. 6, 1933 (2017). https:\/\/doi.org\/10.12688\/f1000research.12934.1","journal-title":"F1000 Res."},{"key":"10097_CR36","unstructured":"Magliacane, S., van Ommen, T., Claassen, T., Bongers, S., Versteeg, P., Mooij, J.M.: Domain adaptation by using causal inference to predict invariant conditional distributions. In: Advances in Neural Information Processing Systems, pp. 10846\u201310856, https:\/\/proceedings.neurips.cc\/paper\/2018\/file\/39e98420b5e98bfbdc8a619bef7b8f61-Paper.pdf (2018)"},{"key":"10097_CR37","unstructured":"Markowetz, F., Grossmann, S., Spang, R.: Probabilistic soft interventions in conditional gaussian networks. In: Tenth International Workshop on Artificial Intelligence and Statistics, Society for Artificial Intelligence and Statistics, pp. 214\u2013221, https:\/\/proceedings.mlr.press\/r5\/markowetz05a.html (2005)"},{"key":"10097_CR38","unstructured":"Mitrovic, J., McWilliams, B., Walker, J., Buesing, L., Blundell, C.: Representation learning via invariant causal mechanisms. arXiv preprint arXiv:2010.07922 (2020)"},{"issue":"10","key":"10097_CR39","doi-asserted-by":"publisher","first-page":"1345","DOI":"10.1109\/TKDE.2009.191","volume":"22","author":"SJ Pan","year":"2009","unstructured":"Pan, S.J., Yang, Q.: A survey on transfer learning. IEEE Trans. Knowl. Data Eng. 22(10), 1345\u20131359 (2009). https:\/\/doi.org\/10.1109\/TKDE.2009.191","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"10097_CR40","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511803161","volume-title":"Causality","author":"J Pearl","year":"2009","unstructured":"Pearl, J.: Causality. Cambridge University Press, Cambridge (2009)"},{"key":"10097_CR41","volume-title":"R: A Language and Environment for Statistical Computing","author":"R Core Team","year":"2020","unstructured":"R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2020)"},{"key":"10097_CR42","first-page":"1","volume":"19","author":"M Rojas-Carulla","year":"2018","unstructured":"Rojas-Carulla, M., Sch\u00f6lkopf, B., Turner, R., Peters, J.: Invariant models for causal transfer learning. J. Mach. Learn. Res. 19, 1\u201334 (2018)","journal-title":"J. Mach. Learn. Res."},{"issue":"2","key":"10097_CR43","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1111\/rssb.12398","volume":"83","author":"D Rothenh\u00e4usler","year":"2021","unstructured":"Rothenh\u00e4usler, D., Meinshausen, N., B\u00fchlmann, P., Peters, J.: Anchor regression: heterogeneous data meet causality. J. R. Stat. Soc. Ser. B 83(2), 215\u2013246 (2021). https:\/\/doi.org\/10.1111\/rssb.12398","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"10097_CR44","doi-asserted-by":"publisher","DOI":"10.4159\/9780674970199","volume-title":"The Seven Pillars of Statistical Wisdom","author":"SM Stigler","year":"2016","unstructured":"Stigler, S.M.: The Seven Pillars of Statistical Wisdom. Harvard University Press, Harvard (2016)"},{"key":"10097_CR45","doi-asserted-by":"publisher","unstructured":"Subbaswamy, A., Saria, S.: From development to deployment: dataset shift, causality, and shift-stable models in health AI. Biostatistics 21(2), 345\u2013352 (2019). https:\/\/doi.org\/10.1093\/biostatistics\/kxz041","DOI":"10.1093\/biostatistics\/kxz041"},{"key":"10097_CR46","doi-asserted-by":"publisher","unstructured":"Therneau, T.M., Grambsch, P.M., Fleming, T.R.: Martingale-based residuals for survival models. Biometrika 77(1), 147\u2013160 (1990). https:\/\/doi.org\/10.1093\/biomet\/77.1.147","DOI":"10.1093\/biomet\/77.1.147"},{"issue":"1","key":"10097_CR47","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. Ser. B 58(1), 267\u2013288 (1996). https:\/\/doi.org\/10.1111\/j.2517-6161.1996.tb02080.x","journal-title":"J. R. Stat. Soc. Ser. B"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-022-10097-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-022-10097-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-022-10097-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T14:49:22Z","timestamp":1700578162000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-022-10097-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,13]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["10097"],"URL":"https:\/\/doi.org\/10.1007\/s11222-022-10097-z","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,13]]},"assertion":[{"value":"22 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 April 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"39"}}