In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling count data with multiple covariates. Furthermore, we provide a detailed explanation of the asymptotic properties of the proposed estimators, including asymptotic biases and mean squared errors. To assess the performance of the estimators, we conduct numerical studies using Monte Carlo simulations and evaluate their simulated relative efficiency. The results demonstrate that the suggested estimators outperform the unrestricted estimator when prior information is taken into account. Additionally, we present an empirical application to demonstrate the practical utility of the suggested estimators.

翻译：本文提出在系数先验信息可得的情况下，将收缩策略应用于Bell回归模型以估计系数。Bell回归模型特别适用于处理含多个协变量的计数数据。我们详细阐述了所提估计量的渐近性质，包括渐近偏差和均方误差。为评估估计量的性能，我们采用蒙特卡洛模拟进行数值研究，并评估其模拟相对效率。结果表明，在考虑先验信息时，所建议的估计量优于无约束估计量。此外，我们通过实证应用展示了所提估计量的实际效用。