A new version of almost unbiased estimator for the Poisson regression model

Abstract

When model of Poisson regression's explanatory variables consist of highly correlated, the widely employed maximum-likelihood estimator is unstable with high variance. As a result, the biased estimators are used to decrease the maximum-likelihood instability and it also produces a reduction of the mean squared error  matrix. For this reason, in this paper, a new biased estimator is suggested and the statistical properties are found. The performance of suggested estimator is studied and compared with other exist estimators using the mean squared error as a criterion for goodness of fit. In order to support the preference of the new estimator in the theoretical aspect, a real example was given represented by fatality resulting from traffic accidents in Sweden.