This paper addressed parameter estimation in the Poisson regression model in the presence of multicollinearity when it is surmised that the parameter vector is restricted to a linear subspace. To improve the efficiency of parameter estimation, we proposed the Stein-Liu and positive Stein-Liu strategies. The proposed estimators’ asymptotic distributional biases and variances were derived, and their variances were compared. The performance of the proposed estimators was investigated through an extensive Monte Carlo simulation study. The suggested estimators were also applied to data from Swedish football. The results confirmed that the performances of our estimators were superior to the unrestricted Liu estimator. As an important result, the Stein-Liu estimators uniformly perform better than the unrestricted Liu estimator.
