On the James-Stein estimator for the poisson regression model

Abstract

The Poisson regression model (PRM) aims to model a counting variable y, which is usually estimated by using maximum likelihood estimation (MLE) method. The performance of MLE is not satisfactory in the presence of multicollinearity. Therefore, we propose a Poisson James-Stein estimator (PJSE) as a solution to the problems of inflated variance and standard error of MLE with multicollinear explanatory variables. For assessing the superiority of proposed estimator, we present a theoretical comparison based on the matrix mean squared error (MMSE) and scalar mean squared error (MSE) criterions. A Monte Carlo simulation study is performed under different conditions in order to investigate the performance of the proposed estimator where MSE is considered as an evaluation criterion. In addition, an aircraft damage data is also considered to assess the superiority of proposed estimator. Based on the results of simulation and real data application, it is shown that the PJSE outperforms the classical MLE and other biased estimation methods in a sense of minimum MSE criterion.

KEYWORDS:

• Maximum likelihood estimation
• Multicollinearity
• Poisson James-Stein estimator
• Poisson regression model