Equality between two general ridge estimators and equivalence of their residual sums of squares

Hirai Mukasa () and Koji Tsukuda ()
Additional contact information
Hirai Mukasa: Kyushu University
Koji Tsukuda: Kyushu University

Statistical Papers, 2025, vol. 66, issue 1, No 27, 20 pages

Abstract: Abstract General ridge estimators are typical linear estimators in a general linear model. The class of them includes some shrinkage estimators in addition to classical linear unbiased estimators such as the ordinary least squares estimator and the weighted least squares estimator. Also, they have some properties such as linear sufficiency and admissibility in the class of linear estimators. We derive necessary and sufficient conditions under which two general ridge estimators coincide. In particular, two noteworthy conditions are added to those from previous studies. The first condition is given as a seemingly column space relationship to the covariance matrix of the error term, and the second one is based on the biases of general ridge estimators. Another problem studied in this paper is to derive an equivalence condition such that equality between two residual sums of squares holds when general ridge estimators are considered. Additionally, we demonstrate some concrete examples for which the equivalence conditions hold.

Keywords: General linear model; Least squares estimator; Residual sum of squares; Ridge estimator; 62J05; 62F10; 62J07 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-024-01644-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01644-z

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-024-01644-z

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().