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

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.