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Ridge-type shrinkage estimators in generalized linear models with an application to prostate cancer data
Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Jönköping University, Jönköping International Business School, JIBS, Statistics. Jönköping University, Jönköping International Business School, JIBS, Economics.ORCID iD: 0000-0002-4535-3630
2019 (English)In: Statistical papers, ISSN 0932-5026, E-ISSN 1613-9798Article in journal (Refereed) Epub ahead of print
Abstract [en]

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. 

Place, publisher, year, edition, pages
Springer, 2019.
Keywords [en]
Generalized linear models, Multicollinearity, Relative efficiency, Ridge regression, Stein-type shrinkage
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hj:diva-46290DOI: 10.1007/s00362-019-01123-wScopus ID: 2-s2.0-85068832733Local ID: ;IHHÖvrigtISOAI: oai:DiVA.org:hj-46290DiVA, id: diva2:1353169
Available from: 2019-09-20 Created: 2019-09-20 Last updated: 2019-09-20

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Månsson, Kristofer

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