A novel modified Liu estimator for the inverse Gaussian regression model to effectively handle multicollinear positive data

Ali T. Hammad; Ehab M. Almetwally; Hisham Mohamed Almongy; Ahmed M. Gemeay; Yousef Alharbi; Ramlah H. Albayyat; Wafa Ali J. Almohri; Manahil SidAhmed Mustafa; Ali T. Hammad; Ehab M. Almetwally; Hisham Mohamed Almongy; Ahmed M. Gemeay; Yousef Alharbi; Ramlah H. Albayyat; Wafa Ali J. Almohri; Manahil SidAhmed Mustafa

doi:10.3934/math.2026293

AIMS Mathematics

2026, Volume 11, Issue 3: 7115-7142. doi: 10.3934/math.2026293

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A novel modified Liu estimator for the inverse Gaussian regression model to effectively handle multicollinear positive data

1.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
4.
Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia
5.
Department of Mathematics, College of Science, Taibah University, Madinah, Saudi Arabia
6.
Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia

Received: 03 February 2026 Revised: 03 March 2026 Accepted: 10 March 2026 Published: 18 March 2026
MSC : 62J12, 62J07, 62J10, 62P10

The inverse Gaussian regression model (IGRM) is a commonly used method for modeling multivariate data where the response variable is positively skewed. Parameter estimation in the IGRM is estimated via the maximum likelihood estimator (MLE). While the MLE demonstrates optimal performance under conditions of independent explanatory variables, its efficacy is substantially compromised in the presence of high correlation between explanatory variables, which is known as multicollinearity. This phenomenon leads to inflated variances and standard errors in the coefficient estimates, thereby undermining their statistical efficiency and reliability. To address this inferential challenge, this study introduced a novel modified Liu estimator specifically designed for the IGRM. The proposed estimator aims to mitigate the adverse effects of multicollinearity and enhance the precision of the regression coefficients. The performance of the proposed estimator was rigorously evaluated against the MLE and other established biased estimators. A comprehensive Monte Carlo simulation was utilized for this assessment, whose results indicate the outperformance of the proposed estimator. To further substantiate the scientific utility of this estimator, two applications utilizing real-world multivariate medical data were conducted; the results of these applications were consistent with and reinforced the findings of the simulation study. The synthesized evidence from the simulation study and real-world data analysis suggests that the proposed estimator consistently outperforms competing estimators for the IGRM, achieving greater stability and reliability in the results.
- inverse Gaussian model,
- multicollinearity,
- biased estimator,
- modified Liu estimators,
- multivariate medical data
Citation: Ali T. Hammad, Ehab M. Almetwally, Hisham Mohamed Almongy, Ahmed M. Gemeay, Yousef Alharbi, Ramlah H. Albayyat, Wafa Ali J. Almohri, Manahil SidAhmed Mustafa. A novel modified Liu estimator for the inverse Gaussian regression model to effectively handle multicollinear positive data[J]. AIMS Mathematics, 2026, 11(3): 7115-7142. doi: 10.3934/math.2026293

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Abstract

The inverse Gaussian regression model (IGRM) is a commonly used method for modeling multivariate data where the response variable is positively skewed. Parameter estimation in the IGRM is estimated via the maximum likelihood estimator (MLE). While the MLE demonstrates optimal performance under conditions of independent explanatory variables, its efficacy is substantially compromised in the presence of high correlation between explanatory variables, which is known as multicollinearity. This phenomenon leads to inflated variances and standard errors in the coefficient estimates, thereby undermining their statistical efficiency and reliability. To address this inferential challenge, this study introduced a novel modified Liu estimator specifically designed for the IGRM. The proposed estimator aims to mitigate the adverse effects of multicollinearity and enhance the precision of the regression coefficients. The performance of the proposed estimator was rigorously evaluated against the MLE and other established biased estimators. A comprehensive Monte Carlo simulation was utilized for this assessment, whose results indicate the outperformance of the proposed estimator. To further substantiate the scientific utility of this estimator, two applications utilizing real-world multivariate medical data were conducted; the results of these applications were consistent with and reinforced the findings of the simulation study. The synthesized evidence from the simulation study and real-world data analysis suggests that the proposed estimator consistently outperforms competing estimators for the IGRM, achieving greater stability and reliability in the results.

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