www.ccsenet.org/ijsp International Journal of Statistics and Probability Vol. 1, No. 1; May 2012 Improved Liu Estimators for the Poisson Regression Model Kristofer Mansson Department of Economics, Finance and Statistics, Jonkoping University Jonkoping, Sweden B. M. Golam Kibria (Corresponding author) Department of Mathematics and Statistics, Florida International University Miami, Florida, USA Par Sjolander Department of Economics, Finance and Statistics, Jonkoping University Jonkoping, Sweden Ghazi Shukur Department of Economics, Finance and Statistics, Jonkoping University Jonkoping, Sweden & Department of Economics and Statistics, Linnaeus University Vaxjo, Sweden Received: February 6, 2012 Accepted: February 16, 2012 Published: May 1, 2012 doi:10.5539/ijsp.v1n1p2 URL: http://dx.doi.org/10.5539/ijsp.v1n1p2 Abstract A new shrinkage estimator for the Poisson model is introduced in this paper. This method is a generalization of the Liu (1993) estimator originally developed for the linear regression model and will be generalized here to be used instead of the classical maximum likelihood (ML) method in the presence of multicollinearity since the mean squared error (MSE) of ML becomes inflated in that situation. Furthermore, this paper derives the optimal value of the shrinkage parameter and based on this value some methods of how the shrinkage parameter should be estimated are suggested. Using Monte Carlo simulation where the MSE and mean absolute error (MAE) are calculated it is shown that when the Liu estimator is applied with these proposed estimators of the shrinkage parameter it always outperforms the ML. Keywords: Estimation, MSE, MAE, Multicollinearity, Poisson, Liu, Simulation AMS Subject classification: Primary 62J07, Secondary 62F10 1. Introduction In the field of economics, health, social and physical sciences, the dependent variable often comes in the form of a non- negative integers or counts. In that situation one often apply the Poisson regression model which is usually estimated by maximum likelihood (ML) where the solution to a non-linear equation is found by applying iterative weighted least square (IWLS). This method has been shown in Mansson and Shukur (2011) to be sensitive to multicollinearity and it becomes difficult to make a valid statistical inference since the mean squared error (MSE) becomes inflated. In Mansson and Shukur (2011), a ridge regression estimator (RRE) was presented for logistic regression which was a generalization of that proposed for linear regression by Hoerl and Kennard (1970). It has been shown that the RRE outperformed the ML. The RRE is effective but as Liu (1993) pointed out it has the disadvantage that the estimated parameters are complicated non-linear functions of the ridge parameter k. Therefore, in this paper another shrinkage estimator for the Poisson model will be proposed which is a generalization of the method proposed for linear regression by Liu (1993). The advantage of this method is that the estimators are a linear function of the shrinkage parameter d. For this reason, this shrinkage estimator has become more popular during recent years (see for examples, Akdeneiz & Kaciranlar, 1995; Kaciranlar, 2 ISSN 1927-7032 E-ISSN 1927-7040