Penalized regression via the restricted bridge estimator

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dc.authoridArashi, Mohammad/0000-0002-5881-9241
dc.authoridYuzbasi, Bahadir/0000-0002-6196-3201
dc.contributor.authorYuzbasi, Bahadir
dc.contributor.authorArashi, Mohammad
dc.contributor.authorAkdeniz, Fikri
dc.date.accessioned2025-03-07T20:21:24Z
dc.date.available2025-03-07T20:21:24Z
dc.date.issued2021
dc.departmentÇağ Üniversitesi
dc.description.abstractThis article is concerned with the bridge regression, which is a special family in penalized regression with penalty function Sigma(p)(j=1) |beta(j) (q) with q > 0, in a linear model with linear restrictions. The proposed restricted bridge (RBRIDGE) estimator simultaneously estimates parameters and selects important variables when a piece of prior information about parameters are available in either low-dimensional or high-dimensional case. Using local quadratic approximation, we approximate the penalty term around a local initial values vector. The RBRIDGE estimator enjoys a closed-form expression that can be solved when q > 0. Special cases of our proposal are the restricted LASSO (q = 1), restricted RIDGE (q = 2), and restricted Elastic Net (1 < q < 2) estimators. We provide some theoretical properties of the RBRIDGE estimator for the low-dimensional case, whereas the computational aspects are given for both low- and high-dimensional cases. An extensive Monte Carlo simulation study is conducted based on different prior pieces of information. The performance of the RBRIDGE estimator is compared with some competitive penalty estimators and the ORACLE. We also consider four real-data examples analysis for comparison sake. The numerical results show that the suggested RBRIDGE estimator outperforms outstandingly when the prior is true or near exact.
dc.description.sponsorshipInonu University Scientific Researches Unit [SUA-2019-1629]
dc.description.sponsorshipThe authors thank the editor and reviewer for their detailed reading of the manuscript and their valuable comments and suggestions that led to a considerable improvement of the paper. Prof. Yuzba was supported by Inonu University Scientific Researches Unit with the project number SUA-2019-1629 during his visit to the University of British Columbia, Vancouver, Canada.
dc.identifier.doi10.1007/s00500-021-05763-9
dc.identifier.endpage8416
dc.identifier.issn1432-7643
dc.identifier.issn1433-7479
dc.identifier.issue13
dc.identifier.scopus2-s2.0-85107873517
dc.identifier.scopusqualityQ1
dc.identifier.startpage8401
dc.identifier.urihttps://doi.org/10.1007/s00500-021-05763-9
dc.identifier.urihttps://hdl.handle.net/20.500.12507/3372
dc.identifier.volume25
dc.identifier.wosWOS:000641235700004
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofSoft Computing
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20241226
dc.subjectBridge regression
dc.subjectRestricted estimation
dc.subjectMachine learning
dc.subjectQuadratic approximation
dc.subjectNewton-Raphson
dc.subjectVariable selection
dc.subjectMulticollinearity
dc.titlePenalized regression via the restricted bridge estimator
dc.typeArticle

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