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：本文研究了伽马回归模型中参数存在线性约束时的多重共线性问题。线性约束来源于先验信息，以确保基于物理现象的科学理论有效性或结构一致性。为对模型进行相关统计推断，应充分考虑模型参数的任何可用知识与先验信息。因此，本文提出一种算法，用于获取受线性不等式约束的伽马回归模型参数的贝叶斯估计量。通过蒙特卡洛模拟及对实际数据集的实证分析，我们证明所提出的估计量在相关性与精确性方面均优于普通估计量，如极大似然估计和岭估计。