Post estimation and prediction strategies in negative binomial regression model

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.

KEYWORDS:

• Negative binomial regression
• preliminary test
• James-Stein rule
• penalty
• asymptotic distributional bias and risk
• Monte Carlo

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research work of Professor S.E. Ahmed was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. Supranee Lisawadi gratefully acknowledges the financial support provided by Thammasat University under the TU Research Scholar.

Notes on contributors

Supranee Lisawadi

Dr. Supranee Lisawadi is the assistant professor at the Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Thailand.

S. E. Ahmed

Dr. S. E. Ahmed is the dean of the Faculty of Mathematics and Science and professor of the Department of Mathematics and Statistics, Brock University, Canada.

Orawan Reangsephet

Dr. Orawan Reangsephet is the lecturer at the Department of Statistics, Faculty of Science, Silpakorn University, Thailand.