{"id":2477,"date":"2025-03-18T07:03:01","date_gmt":"2025-03-18T07:03:01","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/03\/18\/2503-11854\/"},"modified":"2025-03-18T07:03:01","modified_gmt":"2025-03-18T07:03:01","slug":"2503-11854","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/03\/18\/2503-11854\/","title":{"rendered":"Bayes and Biased Estimators Without Hyper-parameter Estimation: Comparable Performance to the Empirical-Bayes-Based Regularized Estimator"},"content":{"rendered":"

Bayes and Biased Estimators Without Hyper-parameter Estimation: Comparable Performance to the Empirical-Bayes-Based Regularized Estimator
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arXiv:2503.11854v1 Announce Type: new
\nAbstract: Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator in terms of minimizing mean squared error (MSE). However, regularized estimators often require hyper-parameter estimation. This paper focuses on ridge regression and the regularized estimator by employing the empirical Bayes hyper-parameter estimator. We utilize the excess MSE to quantify the MSE difference between the empirical-Bayes-based regularized estimator and the maximum likelihood estimator for large sample sizes. We then exploit the excess MSE expressions to develop both a family of generalized Bayes estimators and a family of closed-form biased estimators. They have the same excess MSE as the empirical-Bayes-based regularized estimator but eliminate the need for hyper-parameter estimation. Moreover, we conduct numerical simulations to show that the performance of these new estimators is comparable to the empirical-Bayes-based regularized estimator, while computationally, they are more efficient.<\/div>\n

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\n Yue Ju, Bo Wahlberg, Hr{a}kan Hjalmarsson
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Bayes and Biased Estimators Without Hyper-parameter Estimation: Comparable Performance to the Empirical-Bayes-Based Regularized Estimator arXiv:2503.11854v1 Announce Type: new Abstract: Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator in terms of minimizing mean squared […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,493,494,112],"tags":[695,2014,2055],"class_list":["post-2477","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-cs-sy","category-eess-sy","category-stat-ml","tag-bayes","tag-estimator","tag-regularized"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2477"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=2477"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2477\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2477"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2477"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}