On a class of linear regression methods

In this paper, a unified study is presented for the design and analysis of a broad class of linear regression methods. The proposed general framework includes the conventional linear regression methods (such as the least squares regression and the Ridge regression) and some new regression methods (e...

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Bibliographic Details
Published inJournal of Complexity Vol. 82; p. 101826
Main Authors Wang, Ying-Ao, Huang, Qin, Yao, Zhigang, Zhang, Ye
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2024
Subjects
Asymptotic Gaussian
Consistency
Dynamic
Inverse problems
Linear regression
Regularization
Asymptotic Gaussian
Dynamic
Inverse problems
Linear regression
Regularization
Consistency
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Summary:In this paper, a unified study is presented for the design and analysis of a broad class of linear regression methods. The proposed general framework includes the conventional linear regression methods (such as the least squares regression and the Ridge regression) and some new regression methods (e.g. the Landweber regression and Showalter regression), which have recently been introduced in the fields of optimization and inverse problems. The strong consistency, the reduced mean squared error, the asymptotic Gaussian property, and the best worst case error of this class of linear regression methods are investigated. Various numerical experiments are performed to demonstrate the consistency and efficiency of the proposed class of methods for linear regression.
ISSN:0885-064X
1090-2708
DOI:10.1016/j.jco.2024.101826