Improved Liu Estimators for the Poisson Regression Model

Kristofer Mansson,Par Sjolander,Ghazi Shukur,B M Golam Kibria

doi: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.

Highlights

In the field of economics, health, social and physical sciences, the dependent variable often comes in the form of a nonnegative integers or counts
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
In a Monte Carlo study we evaluate the performance of the ML and the Liu estimator applied with the suggested estimators of the shrinkage parameter

Summary

Introduction

In the field of economics, health, social and physical sciences, the dependent variable often comes in the form of a nonnegative 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 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. This shrinkage estimator has become more popular during recent years

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