Penalized and ridge-type shrinkage estimators in Poisson regression model

The paper considers the problem of estimation of the regression coefficients in a Poisson regression model under multicollinearity situation. We propose non-penalty Stein-type shrinkage ridge estimation approach when it is conjectured that some prior information is available in the form of potential linear restrictions on the coefficients. We establish the asymptotic distributional biases and risks of the proposed estimators and investigate their relative performance with respect to the unrestricted ridge estimator. For comparison sake, we consider the two penalty estimators, namely, least absolute shrinkage and selection operator and Elastic-Net estimators and compare numerically their relative performance with the other listed estimators. Monte-Carlo simulation experiment is conducted to evaluate the performance of each estimator in terms of the simulated relative efficiency. The results show that the shrinkage ridge estimators perform better than the penalty estimators in certain parts of the parameter space. Finally, a real data example is illustrated to evaluate of the proposed methods.