Generalized kibria-lukman estimator for multicollinearity in linear regression models: theoretical insights and comparative analysis
1 Department of Basic Sciences, Babcock University. Ilishan-Remo, Ogun State. Nigeria
2 Department of Mathematical Sciences, Adeleke University, Ede, Osun State. Nigeria.
3 Department of Statistics, University of Fort Hare Alice, Eastern Cape, South Africa.
4 Department of Statistics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
Research Article
International Journal of Science and Technology Research Archive, 2024, 07(02), 114-119.
Article DOI: 10.53771/ijstra.2024.7.2.0073
Publication history:
Received on 13 November 2024; revised on 22 December 2024; accepted on 24 December 2024
Abstract:
Multicollinearity, a common issue in regression models caused by high correlations among explanatory variables, undermines the stability and reliability of traditional estimators like Ordinary Least Squares (OLS). This study investigates the Generalized Kibria-Lukman (GKL) estimator, introduced by Dawoud et al. (2022), which uses a flexible biasing parameter to address the inflated variances typical in multicollinear datasets. Through comprehensive simulation studies and empirical testing, we compare the GKL estimator’s performance with other biased estimators, including ridge regression and the Liu estimator, focusing on Mean Squared Error (MSE) as the primary evaluation metric. The results demonstrate that the GKL estimator consistently achieves lower MSE values, particularly in highly multicollinear conditions, underscoring its effectiveness as a robust alternative for improving accuracy in regression models where traditional methods struggle. These findings highlight the GKL estimator’s potential as a superior choice in complex, multicollinear regression environments.
Keywords:
Multicollinearity; Generalized Kibria-Lukman Estimator; Regression Models; Biasing Parameter; Mean Squared Error (MSE)
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