Owing to the broad applicability of gamma regression, we propose some improved estimators based on the preliminary test and Stein-type strategies to estimate the unknown parameters in a gamma regression model. These estimators are considered when it is suspected that the parameters may be restricted to a subspace of the parameter space. Two penalty estimators such as LASSO and ridge regression are also presented. An asymptotic theory for the preliminary test and Stein-type estimators is developed, and asymptotic distributional bias and asymptotic quadratic risk of the proposed estimators are obtained. Comprehensive Monte-Carlo simulation experiments are conducted. Comparisons are then made based on simulated relative efficiency to clarify the performance of the proposed estimators. Practitioners are recommended to use the positive-part Stein-type estimator since its performance is robust irrespective of the reliability of the subspace information. A real data on prostate cancer is considered to illustrate the performance of the proposed estimators.

中文翻译：

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伽马回归模型中初步检验、Stein 型和惩罚估计量的比较

由于 gamma 回归的广泛适用性，我们基于初步测试和 Stein 型策略提出了一些改进的估计器来估计 gamma 回归模型中的未知参数。当怀疑参数可能被限制在参数空间的子空间中时，会考虑这些估计量。还介绍了两个惩罚估计器，例如 LASSO 和岭回归。建立了初步检验和 Stein 型估计量的渐近理论，并获得了所提出估计量的渐近分布偏差和渐近二次风险。进行了全面的蒙特卡罗模拟实验。然后根据模拟的相对效率进行比较，以阐明建议的估计器的性能。建议从业者使用正部分 Stein 型估计器，因为无论子空间信息的可靠性如何，它的性能都是稳健的。考虑到前列腺癌的真实数据来说明所提议的估计器的性能。