Employing Several Methods to Estimate the Generalized Liu Parameter in Multiple Linear Regression Model

Najlaa Saad Ibrahim Alsharabi, Rasha Raad Al-Mola, Rehad Emad Slewa Yonan, Zakariya Yahya Algamal


Multiple linear interferences are a fundamental obstacle in many standard models. This problem appears as a result of linear relationships between two explanatory variables or more. Simulation results show that the generalized Liu regression model was the best and that the contraction parameter proposed was more efficient than the methods presented. As the error variance increases, the value (MSE) increases. When this problem exists in the data, the estimator of the ordinary least squares method will fail because one of the basic assumptions of the method has not been fulfilled. The normal least squares, which state that there is no linear correlation between the explanatory variables, will not get an estimator with the Best Linear Unbiased Estimator (BLUE) feature. The least-squares regression method and the generalized Liu regression method were compared by taking several methods for the generalized Liu parameters and selecting the best contraction parameter for the Liu regression model. The study aims to address the problem of multiple linear interferences by using the general Liu estimator and making a comparison between the methods for estimating the Liu parameter, where several methods were presented, and the best method for estimating the Liu parameter was chosen according to the standard of the sum of error squares as well as a comparison between these methods and the conventional method. Simulation results showed that the generalized Liu coefficient estimate was the best for having the lowest values (MSE) and that the best shrinkage parameter is (G4), the work-based approach.


Unbiased estimator; generalized Liu; regression; shrinkage parameter.

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Akram, M. N., Amin, M., & Qasim, M. (2020). A new Liu-type estimator for the Inverse Gaussian Regression Model A new Liu-type estimator for the Inverse Gaussian Regression. Journal of Statistical Computation and Simulation, 0(0), 1–20. https://doi.org/10.1080/00949655.2020.1718150.

Al-taie, B. F. K. (2017). The Role of Tax Havens in the Tax Revenue Development and Its Reflection on the Public Revenues of the Developing Countries : An Empirical Study in Iraq ( 2004-2014 ) Hakeem Hammood Flayyih Noor Abbas Hussein. 8(2), 289–300 https://doi.org/10.5901/mjss.2017.v8n2p289.

Akram, M. N., Amin, M. & Amanullah, M. (2021). James Stein Estimator for the Inverse Gaussian Regression Model. Iranian Journal of Science and Technology, Transactions A: Science 45,1389–1403. https://doi.org/10.1007/s40995-021-01133-0.

Amin, M., Qasim, M. & Amanullah, M. (2019). Performance of Asar and Genç and Huang and Yang’s Two-Parameter Estimation Methods for the Gamma Regression Model. Iran J Sci Technol Trans Sci 43, 2951–2963. https://doi.org/10.1007/s40995-019-00777-3

Feng, F., Teng, S., Liu, K., Xie, J., Xie, Y., Liu, B., & Li, K. (2020). Co-estimation of lithium-ion battery state of charge and state of temperature based on a hybrid electrochemical-thermal-neural-network model. Journal of Power Sources, 455(February), 227935. https://doi.org/10.1016/j.jpowsour.2020.227935.

Hidayat, R., Tri, I., Yanto, R., & Azhar, A. (2021). Similarity measure fuzzy soft set for phishing detection. 7(1), 101–111.

Hoerl, A. & Kennard, R. (1970). Ridge regression: biased estimation for non-orthogonal problems. Technometrics 12, 55–67.

Jadhav, N.H. On linearized ridge logistic estimator in the presence of multicollinearity. Comput Stat 35, 667–687 (2020). https://doi.org/10.1007/s00180-019-00935-6.

Kaciranlar, S. (2003). Liu estimator in the general linear regression model. Journal of Applied Statistical Science 13, 229–234.

Kadhim, H., Ishak, M. R., Sapuan, S. M., & Yidris, N. (2020). Conceptual design of the cross-arm for the application in the transmission towers by using TRIZ – morphological chart – ANP methods. Integrative Medicine Research, 9(4), 9182–9188. https://doi.org/10.1016/j.jmrt.2020.05.129

Kadhim, H., Ishak, M. R., Sapuan, S. M., Yidris, N., & Fattahi, A. (2020). Experimental and numerical investigation of the mechanical behavior of full-scale wooden cross arm in the transmission towers in terms of load-deflection test. Integrative Medicine Research, 9(4),7937–7946. https://doi.org/10.1016/j.jmrt.2020.04.069.

Kadhim, H., Sadeq, S., Marwah, S., Rustem, H. A., Vasilii, R. M., & Troitskii, I. (2021). Role of initial stored energy on hydrogen microalloying of ZrCoAl (Nb ) bulk metallic glasses. Applied Physics A, 127(1), 1–7. https://doi.org/10.1007/s00339-020-04191-0.

Kibria, B. M. G. (2020). A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications.

Li, X., Zhang, H., Zhang, R., Liu, Y., & Nie, F. (2019). Generalized Uncorrelated Regression with Adaptive Graph for Unsupervised Feature Selection. 30(5), 1587–1595.

Li, N., Yang, H. Nonnegative estimation, and variable selection under minimax concave penalty for sparse high-dimensional linear regression models. Stat Papers 62, 661–680 (2021). https://doi.org/10.1007/s00362-019-01107-w.

Liu, J., Zhou, J., Yao, J., Zhang, X., Li, L., Xu, X., He, X., & Wang, B. (2020). Science of the Total Environment Impact of meteorological factors on the COVID-19 transmission: A multi- city study in China. Science of the Total Environment, 726, 138513. https://doi.org/10.1016/j.scitotenv.2020.138513.

Liu, S., Long, M., Wang, J., & Jordan, M. I. (2018). Generalized Zero-Shot Learning with Deep Calibration Network. NeurIPS.

Liu, Y., Wu, J., Wang, Z., Lu, X., Avdeev, M., Shi, S., Wang, C., & Yu, T. (2020). Acta Materialia Predicting creep rupture life of Ni-based single crystal superalloys using divide-and-conquer approach-based machine learning. Acta Materialia, 195, 454–467. https://doi.org/10.1016/j.actamat.2020.05.001.

Lukman, A. F., Emmanuel, A., Clement, O.A. & Ayinde, K. (2020). A Modified Ridge-Type Logistic Estimator. . Iranian Journal of Science and Technology, Transactions A: Science 44,437-443. https://doi.org/10.1007/s40995-020-00845-z.

Ma, L. (2018). Deep Non-Blind Deconvolution via Generalized Low-Rank Approximation. Nips.

Månsson, K., Kibria, B. M. G. (2021). Estimating the Unrestricted and Restricted Liu Estimators for the Poisson Regression Model: Method and Application. Comput Econ 58, 311–326. https://doi.org/10.1007/s10614-020-10028-y

Qasim, M., Amin, M., & Amanullah, M. (2018). On the performance of some new Liu parameters for the gamma regression model. Journal of Statistical Computation and Simulation, 0(0), 1–16. https://doi.org/10.1080/00949655.2018.1498502.

Qasim, M., Månsson, K., Amin, M. et al. Biased Adjusted Poisson Ridge Estimators-Method and Application. Iran J Sci Technol Trans Sci 44, 1775–1789 (2020). https://doi.org/10.1007/s40995-020-00974-5.

Raheemah, S. H., Fadheel, K. I., Hassan, Q. H., Aned, A. M., Al-taie, A. A. T., & Kadhim, H. (2021). Science & Technology Numerical Analysis of the Crack Inspections Using Hybrid Approach for the Application the Circular Cantilever Rods. 29(2), 1109–1117..

Yanto, Iwan & Sutoyo, Edi & Rahman, Arif & Hidayat, Rahmat & Ramli, Ts. Azizul Azhar & Md Fudzee, Mohd Farhan. (2020). Classification of Student Academic Performance using Fuzzy Soft Set. 1-6. 10.1109/ICoSTA48221.2020.1570606632.

Thamer N. & Alsharabi N. (2021). Predicting Time Series of Temperature in Nineveh Using The Conversion Function Models. International Journal on Advanced Science Engineering Information technology.11(2).

Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society B 58(1):267–288.

Wang, L., Long, F., Liao, W., & Liu, H. (2020). Bioresource Technology Prediction of anaerobic digestion performance and identification of critical operational parameters using machine learning algorithms. Bioresource Technology, 298(November 2019), 122495. https://doi.org/10.1016/j.biortech.2019.122495.

Wei, J., Liu, Y., Zhu, Y., Qian, J., Ye, R., Li, C., Ji, X., Liu, Y., Jia, N., Li, S., Li, X., Xue, F., & Zhao, L. (2020). International Journal of Hygiene and Environmental Health Impacts of transportation and meteorological factors on the transmission of. 230(June). https://doi.org/10.1016/j.ijheh.2020.113610.

Zamunér, A. R., & Lu, C. (2019). HbA1C Variability Is Strongly Associated With the Severity of Cardiovascular Autonomic Neuropathy in Patients With Type 2 Diabetes After Longer Diabetes Duration. 13(May),1–8. https://doi.org/10.3389/fnins.2019.00458.

DOI: http://dx.doi.org/10.18517/ijaseit.12.6.14789


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