Ridge-type shrinkage estimators in generalized linear models with an application to prostate cancer data

M. Nooi Asl, H. Bevrani, R. Arabi Belaghi () and K. Mansson
Additional contact information
M. Nooi Asl: University of Tabriz
H. Bevrani: University of Tabriz
R. Arabi Belaghi: University of Tabriz
K. Mansson: Jonkoping University

Statistical Papers, 2021, vol. 62, issue 2, No 20, 1043-1085

Abstract: Abstract This paper is concerned with the estimation of the regression coefficients for the generalized linear models in the situation where a multicollinear issue exists and when it is suspected that some of the regression coefficients may be restricted to a linear subspace. Accordingly, as a solution to this issue, we propose a new Stein-type shrinkage ridge estimation approach. We provide the analytic expressions for the asymptotic biases and risks of the proposed estimators and investigate their relative performance with respect to the unrestricted ridge regression estimator. Monte-Carlo simulation studies are conducted to appraise the performance of the underlying estimators in terms of their simulated relative efficiencies. It is clear from both the analytical results and the simulation study that the Stein-type shrinkage ridge estimators dominate the usual ridge regression estimator in the entire parameter space. Finally an empirical application is provided where prostate cancer data is analyzed to show the practical usefulness of the suggested approach. Based on the results from the different parts of this paper, we find that the new method developed would be useful for the practitioners in various research areas such as economics, insurance data and medicine.

Keywords: Multicollinearity; Generalized linear models; Ridge regression; Stein-type shrinkage; Relative efficiency; Primary 62J07; Secondary 62F30 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00362-019-01123-w 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:62:y:2021:i:2:d:10.1007_s00362-019-01123-w

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

DOI: 10.1007/s00362-019-01123-w

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 ().