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.

中文翻译：

---

广义线性模型中的脊型收缩估计器，适用于前列腺癌数据

本文关注的是在存在多重共线性问题的情况下以及当怀疑某些回归系数可能被限制在线性子空间时，广义线性模型的回归系数的估计。因此，为了解决这个问题，我们提出了一种新的 Stein 型收缩脊估计方法。我们提供了所提出估计量的渐近偏差和风险的解析表达式，并研究了它们相对于无限制岭回归估计量的相对性能。进行蒙特卡罗模拟研究以根据模拟的相对效率来评估基础估计器的性能。从分析结果和模拟研究中可以清楚地看出，Stein 型收缩脊估计量在整个参数空间中主导了通常的脊回归估计量。最后提供了一个经验应用，其中分析了前列腺癌数据以显示所建议方法的实际用途。基于本文不同部分的结果，我们发现所开发的新方法将对经济学、保险数据和医学等各个研究领域的从业者有用。