Instrumental variable based SEE variable selection for Poisson regression models with endogenous covariates

In the case of containing endogenous covariates, we study the variable selection problem for Poisson regression models based on the instrumental variable adjustment technology. By using a modified smooth-threshold estimating equation technology, we propose an instrumental variable based variable selection procedure. The proposed method can attenuate the effect of endogenous covariates, and is easy for application in practice. We also prove that this variable selection procedure is consistent in theory. Some simulations and a real data analysis are given to evaluate the performance of the proposed method, and simulation results show that the proposed variable selection procedure is workable.