In this paper, we consider the multicollinearity problem in the gamma regression model when model parameters are linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories or structural consistency based on physical phenomena. In order to make relevant statistical inference for a model any available knowledge and prior information on the model parameters should be taken into account. This paper proposes therefore an algorithm to acquire Bayesian estimator for the parameters of a gamma regression model subjected to some linear inequality restrictions. We then show that the proposed estimator outperforms the ordinary estimators such as the maximum likelihood and ridge estimators in term of pertinence and accuracy through Monte Carlo simulations and application to a real dataset.

翻译：在本文中,当模型参数受到线性限制时,我们考虑伽马回归模型中的多线性问题。线性限制来自先前的信息,以确保科学理论或基于物理现象的结构一致性的有效性。为了对模型进行相关的统计推断,应考虑关于模型参数的任何现有知识和先前信息。因此,本文件提出一种算法,以获得受某种线性不平等限制的伽马回归模型参数的巴耶斯估计器。然后,我们表明,拟议的估计器超过了普通估计器,例如,通过蒙特卡洛模拟和对真实数据集的应用,在适切性和准确性方面的最大可能性和海脊估计器。</s>