Estimation Strategies in Poisson Regression Models

Abstract

We consider the application of shrinkage and penalty estimation for a Poisson regression model. We present a large sample theory for the full model, submodel, and shrinkage estimators in terms of their respective asymptotic bias and risk. Generally speaking, shrinkage estimators are more efficient than the full model estimator. Nowadays, variable selection is of fundamental importance for modeling and data analysis. A number of variable selection approaches have been proposed in the literature. On the other hand, absolute penalty estimation strategy is useful for simultaneous variable selection and estimation. For this purpose, we consider three penalty estimators, namely, LASSO, adaptive LASSO, and SCAD. We assess the relative performance of the penalty estimators with the shrinkage estimators using Monte Carlo simulation. The relative performance of each estimation strategy is given in terms of a simulated mean squared error. The simulation results reveal that shrinkage method is an effective consistent model selection technique and is comparable to the LASSO, adaptive LASSO, and SCAD when the model is sparse and number predictors in the model is weak. Finally, the listed estimation strategies are appraised through the application to two real data sets.