In this study, we proposed some ridge estimators by considering the work of Månsson (Econ Model 29(2):178–184, 2012 ), Dorugade (J Assoc Arab Univ Basic Appl Sci 15:94–99, 2014 ) and some others for the gamma regression model (GRM). The GRM is a special form of the generalized linear model (GLM), where the response variable is positively skewed and well fitted to the gamma distribution. The commonly used method for estimation of the GRM coefficients is the maximum likelihood (ML) estimation method. The ML estimation method perform better, if the explanatory variables are uncorrelated. There are the situations, where the explanatory variables are correlated, then the ML estimation method is incapable to estimate the GRM coefficients. In this situation, some biased estimation methods are proposed and the most popular one is the ridge estimation method. The ridge estimators for the GRM are proposed and compared on the basis of mean squared error (MSE). Moreover, the outperforms of proposed ridge estimators are also calculated. The comparison has done using a Monte Carlo simulation study and two real data sets. Results show that Kibria’s and Månsson and Shukur’s methods are preferred over the ML method.

中文翻译：

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伽马回归模型的一些脊估计器的性能

在这项研究中，我们通过考虑 Månsson (Econ Model 29(2):178-184, 2012 ), Dorugade (J Assoc Arab Univ Basic Appl Sci 15:94-99, 2014 ) 和其他一些人的工作提出了一些岭估计量用于伽马回归模型 (GRM)。GRM 是广义线性模型 (GLM) 的一种特殊形式，其中响应变量呈正偏态并很好地拟合了伽马分布。常用的估计 GRM 系数的方法是最大似然 (ML) 估计方法。如果解释变量不相关，则 ML 估计方法性能更好。在某些情况下，解释变量是相关的，则 ML 估计方法无法估计 GRM 系数。在这种情况下，提出了一些有偏估计方法，其中最流行的是岭估计方法。在均方误差 (MSE) 的基础上提出并比较了 GRM 的脊估计量。此外，还计算了所提出的脊估计器的表现。比较是使用蒙特卡罗模拟研究和两个真实数据集完成的。结果表明 Kibria 和 Månsson 以及 Shukur 的方法优于 ML 方法。