We propose Stein-type estimators for zero-inflated Bell regression models by incorporating information on model parameters. These estimators combine the advantages of unrestricted and restricted estimators. We derive the asymptotic distributional properties, including bias and mean squared error, for the proposed shrinkage estimators. Monte Carlo simulations demonstrate the superior performance of our shrinkage estimators across various scenarios. Furthermore, we apply the proposed estimators to analyze a real dataset, showcasing their practical utility.

翻译：我们通过纳入模型参数信息，为零膨胀贝尔回归模型提出了斯坦因型估计量。这些估计量结合了无约束估计量和约束估计量的优势。我们推导了所提出的收缩估计量的渐近分布性质，包括偏差和均方误差。蒙特卡洛模拟表明，我们的收缩估计量在各种情景下均具有优越性能。此外，我们将所提出的估计量应用于真实数据集的实证分析，展示了其实用价值。