Jackknifed Liu-type estimator in the negative binomial regression model

The Liu estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of Inter-correlated (multicollinearity). The negative binomial regression model is a well-known model in the application when the response variable is non-negative integers or counts. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator of the negative binomial coefficients. To overcome this problem, a negative binomial Liu estimator has been proposed by numerous researchers. In this paper, a Jackknifed Liu-type negative binomial estimator (JNBLTE) is proposed and derived. The idea behind the JNBLTE is to decrease the shrinkage parameter and, therefore, the resultant estimator can be better with a small amount of bias. Our Monte Carlo simulation results suggest that the JNBLTE estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the JNBLTE estimator outperforms both the negative binomial Liu estimator and maximum likelihood estimators in terms of predictive performance.