Post estimation and prediction strategies in negative binomial regression model. (2nd November 2021) - Lisawadi, Supranee; Ahmed, S. E.; Reangsephet, Orawan
ABSTRACT: We addressed parameter estimation for low-dimensional and high-dimensional negative binomial regression models in the presence of overfitting and uncertainty about the subspace information. We proposed novelty parameter estimation based on linear shrinkage, preliminary test, James–Stein rule, and penalty strategies, outperforming the classical maximum likelihood. The asymptotic distributional bias and risk were derived to explore and compare the theoretical predictions of the proposed estimators. A numerical comparison of the performance of the proposed estimators was also studied via Monte Carlo simulations and real application to confirm the theoretical results. Based on our findings, estimators based on the preliminary test and James–Stein rule strategies were most effective at addressing the overfitting problem when the accuracy of the subspace information was unknown.