Liu-type Negative Binomial Regression: A Comparison of Recent Estimators and Applications

TL;DR

This paper proposes a new biased estimator for negative binomial regression that reduces variance and improves stability in the presence of multicollinearity, supported by theoretical analysis, simulations, and real data application.

Contribution

Introduces a Liu-type biased estimator for negative binomial regression, generalizing previous linear model estimators to address multicollinearity issues.

Findings

The new estimator has lower mean squared error than existing methods.

Theoretical comparisons show improved variance properties.

Simulation results confirm better performance in practice.

Abstract

This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is inflated when there is multicollinearity between the explanatory variables, a new biased estimator is proposed to solve the problem and decrease the variance of MLE in order to make stable inferences. Moreover, we obtain some theoretical comparisons between the new estimator and some others via matrix mean squared error (MMSE) criterion. Furthermore, a Monte Carlo simulation study is designed to evaluate performances of the estimators in the sense of mean squared error. Finally, a real data application is used to illustrate the benefits of new estimator.