A new linearized ridge Poisson estimator in the presence of multicollinearity

Abstract

Poisson regression is a very commonly used technique for modeling the count data in applied sciences, in which the model parameters are usually estimated by the maximum likelihood method. However, the presence of multicollinearity inflates the variance of maximum likelihood (ML) estimator and the estimated parameters give unstable results. In this article, a new linearized ridge Poisson estimator is introduced to deal with the problem of multicollinearity. Based on the asymptotic properties of ML estimator, the bias, covariance and mean squared error of the proposed estimator are obtained and the optimal choice of shrinkage parameter is derived. The performance of the existing estimators and proposed estimator is evaluated through Monte Carlo simulations and two real data applications. The results clearly reveal that the proposed estimator outperforms the existing estimators in the mean squared error sense.

KEYWORDS:

• Poisson regression
• multicollinearity
• ridge Poisson estimator
• linearized ridge regression estimator
• mean squared error

Mathematics Subject Classifications:

• 62J07
• 62F10

Acknowledgements

The author thanks editor, associate editor and two anonymous referees for their valuable comments and suggestions which lead to considerable improvement in the present version of the paper. This work was partially supported by Shivaji University, Kolhapur, India under Research Initiation Scheme (Grant No. SU/C&U.D.Section/94/231).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Shivaji University, Kolhapur, Maharashtra, INDIA [grant number SU/C&U.D.Section/94/231].