A new class of Poisson Ridge-type estimator

Author:

Ertan EsraORCID,Akay Kadri UlaşORCID

Abstract

AbstractThe Poisson Regression Model (PRM) is one of the benchmark models when analyzing the count data. The Maximum Likelihood Estimator (MLE) is used to estimate the model parameters in PRMs. However, the MLE may suffer from various drawbacks that arise due to the existence of multicollinearity problems. Many estimators have been proposed as alternatives to each other to alleviate the multicollinearity problem in PRM, such as Poisson Ridge Estimator (PRE), Poisson Liu Estimator (PLE), Poisson Liu-type Estimator (PLTE), and Improvement Liu-Type Estimator (ILTE). In this study, we define a new general class of estimators which is based on the PRE as an alternative to other existing biased estimators in the PRMs. The superiority of the proposed biased estimator over the other existing biased estimators is given under the asymptotic matrix mean square error sense. Furthermore, two separate Monte Carlo simulation studies are implemented to compare the performances of the proposed biased estimators. Finally, the performances of all considered biased estimators are shown in real data.

Publisher

Springer Science and Business Media LLC

Subject

Multidisciplinary

Reference36 articles.

1. Winkelmann, R. Econometric Analysis of Count Data. (Springer Science & Business Media, 2008).

2. Hilbe, J. M. Modeling Count Data (Cambridge University Press, 2014).

3. Myers, R. H., Montgomery, D. C., Vining, G. G. & Robinson, T. J. Generalized Linear Models: With Applications in Engineering and the Sciences (Wiley, 2012).

4. Dunn, P. K. & Smyth, G. K. Generalized Linear Models with Examples in R (Springer, 2018).

5. Akay, K. U. & Ertan, E. A new Liu-type estimator in Poisson regression models. Hacet. J. Math. Stat. 51(5), 1484–1503 (2022).

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