Abstract

Generalized linear models (GLM) applications have become very popular in recent years. However, if there is a high degree of relationship between the independent variables, the problem of multicollinearity arises in these models. In this paper, we introduce new first-order approximated (FOA) estimators in the case of gamma distributed response variables in GLMs. Also, the generalization of some estimation methods for ridge and Liu parameters in gamma regression models (GRM) are provided. The superiority of these estimators is assessed by the estimated mean squared error (EMSE) via Monte Carlo simulation study where the response follows a gamma distribution with the log link function. We finally consider a real data application. The proposed estimators are compared and interpreted.

摘要

近年来，广义线性模型（GLM）应用变得非常流行。然而，如果自变量之间存在高度相关性，这些模型就会出现多重共线性问题。在本文中，我们在 GLM 中的伽马分布响应变量的情况下引入了新的一阶近似 (FOA) 估计器。此外，还提供了伽玛回归模型（GRM）中岭和刘参数的一些估计方法的推广。这些估计量的优越性通过蒙特卡罗模拟研究的估计均方误差 (EMSE) 进行评估，其中响应遵循具有对数链接函数的伽马分布。我们最终考虑一个真实的数据应用。对所提出的估计量进行了比较和解释。