Selection of A New Biasing Parameter for the Jackknife Kibria-Lukman Estimator for the Negative Binomial Regression Model

Résumé fourni par la source

The negative binomial regression model (NBRM) is a generalized linear model that relaxes the restrictive assumption of the Poisson regression model when the variance is equal to the mean. The estimation of the parameters of the NBRM is obtained using the maximum likelihood (ML) method. Maximum likelihood estimator becomes unstable when the explanatory variables are linearly dependent, a situation known as multicollinearity. Based on this, we developed a new estimator called modified jackknifed Negative Binomial Kibria Lukman (MJNBKL) estimator for the radiation of multicollinearity in NBRM using four different biasing (shrinkage) parameters. We establish an improvement condition for MJNBKL estimator over the existing estimators. The performance MJNBKL estimator was ascertained by comparing it with the existing estimators through a Monte Carlo simulation study and the use of two real life application datasets. The superiority condition for MJNBKL was established and the properties were also derived. The results of the simulation and real-life application show that MJNBKL estimator outperformed the other estimators compared with by having the smallest mean square error (MSE) across all sample sizes and different levels of correlation was used for the four biasing parameters. The third biasing parameter which is k3 is the optimal biasing parameter with the lowest MSE.

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