Optimal model averaging for divergent-dimensional Poisson regressions

This paper proposes a new model averaging method to address model uncertainty in Poisson regressions, allowing the dimension of covariates to increase with the sample size. We derive an unbiased estimator of the Kullback-Leibler (KL) divergence to choose averaging weights. We show that when all candidate models are misspecified, the proposed estimate is asymptotically optimal by achieving the least KL divergence among all possible averaging estimators. In another situation where correct models exist in the model space, our method can produce consistent coefficient estimates. We apply the proposed techniques to study the determinants and predict corporate innovation outcomes measured by the number of patents.