{"id":25480,"date":"2021-10-18T12:40:09","date_gmt":"2021-10-18T10:40:09","guid":{"rendered":"https:\/\/cio.umh.es\/?p=25480"},"modified":"2022-01-18T12:42:56","modified_gmt":"2022-01-18T11:42:56","slug":"burgard-j-p-krause-j-kreber-d-morales-d-2021-the-generalized-equivalence-of-regularization-and-min-max-robustification-in-linear-mixed-models-statistical-papers-62-62857","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2021\/10\/18\/burgard-j-p-krause-j-kreber-d-morales-d-2021-the-generalized-equivalence-of-regularization-and-min-max-robustification-in-linear-mixed-models-statistical-papers-62-62857\/","title":{"rendered":"Burgard, J.P., Krause, J., Kreber, D., Morales, D. (2021) \u00abThe generalized equivalence of regularization and min\u2013max robustification in linear mixed models\u00bb, Statistical Papers, 62 (6):2857\u20132883"},"content":{"rendered":"<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Jan Pablo Burgard, Joscha Krause (Department of Economic and Social Statistics, Trier University), Dennis Kreber (Department of Operations Research, Trier University) and <\/strong><strong>Domingo Morales (Operations Research Center, University Miguel Hern\u00e1ndez of Elche)<\/strong><\/p>\n<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Abstract: <\/strong>The connection between regularization and min\u2013max robustification in the presence of unobservable covariate measurement errors in linear mixed models is addressed. We prove that regularized model parameter estimation is equivalent to robust loss minimization under a min\u2013max approach. On the example of the LASSO, Ridge regression, and the Elastic Net, we derive uncertainty sets that characterize the feasible noise that can be added to a given estimation problem. These sets allow us to determine measurement error bounds without distribution assumptions. A conservative Jackknife estimator of the mean squared error in this setting is proposed. We further derive conditions under which min-max robust estimation of model parameters is consistent. The theoretical findings are supported by a Monte Carlo simulation study under multiple measurement error scenarios.<\/p>","protected":false},"excerpt":{"rendered":"<p>Jan Pablo Burgard, Joscha Krause (Department of Economic and Social Statistics, Trier University), Dennis Kreber (Department of Operations Research, Trier University) and Domingo Morales (Operations Research Center, University Miguel Hern\u00e1ndez of Elche)<br \/>\nAbstract: The connection between regularization and min\u2013max robustification in the presence of unobservable covariate measurement errors in linear mixed models is addressed. We prove [&#8230;]<\/p>","protected":false},"author":5675,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[369888],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25480"}],"collection":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/users\/5675"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=25480"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25480\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=25480"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=25480"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=25480"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}