Developing robust ridge estimators for Poisson regression model

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Abstract
The Poisson regression model (PRM) is the standard statistical method of analyzing count data, and it is estimated by a Poisson maximum likelihood (PML) estimator. Such an estimator is affected by outliers, and some robust Poisson regression estimators have been proposed to solve this problem. PML estimators are also influenced by multicollinearity. Biased Poisson regression estimators have been developed to address this problem, including Poisson ridge regression and Poisson almost unbiased ridge estimators. However, the above mentioned estimators do not deal with outliers and multicollinearity problems together in a PRM. Therefore, we propose two robust ridge estimators to deal with the two problems simultaneously in the PRM, namely, the robust Poisson ridge regression (RPRR) estimator and the robust Poisson almost unbiased ridge (RPAUR) estimator. Theoretical comparisons and Monte‐Carlo simulations are conducted to investigate the performance of the proposed estimators relative to the performance of other approaches to PRM parameter estimation. The simulation results indicate that the RPAUR estimator outperforms the other estimators in all situations where both problems exist. Finally, real data are used to confirm the results of this paper.

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