Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Oranye Henrietta E
ORCID logo ,
Adejuwon Samuel O
,
Arum Kingsley C
* ORCID logo ,
Ugwuowo Fidelis I
,
Ugah Tobias E
,
Adegoke Taiwo M
,
Sule Omeiza B
Version 1 : Received: 4 July 2023 / Approved: 6 July 2023 / Online: 6 July 2023 (08:58:10 CEST)

How to cite: E, O.H.; O, A.S.; C, A.K.; I, U.F.; E, U.T.; M, A.T.; B, S.O. Selection of A New Biasing Parameter for the Jackknife Kibria-Lukman Estimator for the Negative Binomial Regression Model. Preprints 2023, 2023070405. https://doi.org/10.20944/preprints202307.0405.v1 E, O.H.; O, A.S.; C, A.K.; I, U.F.; E, U.T.; M, A.T.; B, S.O. Selection of A New Biasing Parameter for the Jackknife Kibria-Lukman Estimator for the Negative Binomial Regression Model. Preprints 2023, 2023070405. https://doi.org/10.20944/preprints202307.0405.v1

Abstract

The negative binomial regression model (NBRM) is a generalized linear model which relaxes the restrictive assumption by 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 superiority condition for MJNBKL estimator over the ones. The performance MJNBKL estimator was ascertained by comparing it with the existing ones through a Monte Carlo simulation study and two real life application datasets. The results of the simulation and real life application show that MJNBKL estimator outperformed the other estimators compared with by having the smallest MSE across all sample sizes and for different levels of correlation for the four biasing parameters used and the third biasing parameter is the optimal shrinkage parameter with the lowest MSE.

Keywords

Jackknife; Kibria-Lukman; estimator; Maximum Likelihood; Negative Binomial regression

Subject

Computer Science and Mathematics, Applied Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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