On the biased Two-Parameter Estimator to Combat Multicollinearity in Linear Regression Model

Authors

  • Janet Iyabo Idowu Department of Statistics, Ladoke Akintola University of Technology, Ogbomoso, Oyo State, Nigeria
  • Olasunkanmi James Oladapo Department of Statistics, Ladoke Akintola University of Technology, Ogbomoso, Oyo State, Nigeria
  • Abiola Timothy Owolabi Department of Statistics, Ladoke Akintola University of Technology, Ogbomoso, Oyo State, Nigeria
  • Kayode Ayinde Department of Statistics, Federal University of Technology, Akure, Nigeria

Keywords:

Multicollinearity, Ordinary least-squares, Simulation, Biased two-parameter, Ridge regression estimator

Abstract

The most popularly used estimator to estimate the regression parameters in the linear regression model is the ordinary least-squares (OLS). The existence of multicollinearity in the model renders OLS inefficient. To overcome the multicollinearity problem, a new two-parameter estimator, a biased two-parameter (BTP), is proposed as an alternative to the OLS. Theoretical comparisons and simulation studies were carried out. The theoretical comparison and simulation studies show that the proposed estimator dominated some existing estimators using the mean square error (MSE) criterion. Furthermore, the real-life data bolster both the hypothetical and simulation results. The proposed estimator is preferred to OLS and other existing estimators when multicollinearity is present in the model.

 

Dimensions

D. N. Gujarati, Basic Econometrics, McGraw-Hill, New York, NY, USA (1995).

A. F. Lukman, Classification-Based Ridge, Lambert Academic Publishing (2018).

K. Ayinde, A. F. Lukman, O. O. Alabi & H, A. Bello, ”A New Approach of Principal Component Regression Estimator with Applications to Collinear Data”, International Journal of Engineering Research and Technology 13 (2020).

C. Stein, ”Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability”, University California Press (1956) 197.

W. F. Massy, ”Principal components regression in exploratory statistical research”, Journal of the American Statistical Association 60 (1965) 234.

H.Wold, Partial least squares, In Kotz, Samuel; Johnson, Norman L. (eds.)”, Encyclopedia of statistical sciences, New York: Wiley 6 (1985) 581.

A. E. Hoerl & R. W. Kennard, ”Ridge regression: biased estimation for nonorthogonal problems”, Technometrics 12 (1970) 55.

K. Liu, ”A new class of biased estimate in linear regression”, Communications in Statistics- Theory and Methods 22 (1993) 393.

B. Swindel, ”Good ridge estimators based on prior information”, Communications in Statistics - Theory and Methods A5 (1976) 1065.

M. R. O¨ zkale & S. Kac¸iranlar, ”The restricted and unrestricted two-parameter estimators”, Communications in Statistics - Theory and Methods 36 (2007) 2707.

B. M. G. Kibria & A. F. Lukman, ”A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications”, Scientifica (2020) 1.

I. Dawoud & B. M. G. Kibria, ”A New Biased Estimator to Combat the Multicollinearity of the Gaussian Linear Regression Model”, Stats 3 (2020) 526.

A. T. Owolabi, K. Ayinde, J. I. Idowu, O. J. Oladapo & A. F. Lukman, ”A New Two-Parameter Estimator in the Linear Regression Model with Correlated Regressors”, Journal of Statistics Applications & Probability 11 (2022) 185.

O. J. Oladapo, A. T. Owolabi, J. I. Idowu & K. Ayinde, ”A New Modified Liu Ridge-Type Estimator for the Linear Regression Model: Simulation and Application”, Int J Clin Biostat Biom. 8 (2022) 048.

I. Dawoud, M. R. Abonazel & E. T. Eldin, ”Predictive Performance Evaluation of the Kibria-Lukman Estimator”, WSEAS TRANSACTIONS on MATHEMATICS 21 (2022) 2224.

I. Dawoud, M. R. Abonazel & F. A. Awwad, ”Generalized Kibria-Lukman Estimator: Method, Simulation, and Application”, Front. Appl. Math. Stat. 8 (2022) 880086.

I. Dawoud, M. R. Abonazel, F. A. Awwad & E. Tag Eldin, ”A New Tobit Ridge-Type Estimator of the Censored Regression Model With Multicollinearity Problem”, Front. Appl. Math. Stat. 8 (2022) 952142.

A. F. Lukman, B. M. G. Kibria, K. Ayinde & S. L. Jegede, ”Modified One-Parameter Liu Estimator for the Linear Regression Model”, Modelling and Simulation in Engineering 2020 (2020) 9574304.

K. Liu, ”Using Liu Type Estimator to Combat Collinearity”, Communications in Statistics-Theory and Methods 32 (2003) 1009.

S. Kaciranlar, S. Sakallioglu, F. Akdeniz, G. P. H. Styan & H. J. Werner, ”A new biased estimator in linear regression and a detailed analysis of the widely-analysed dataset on Portland Cement”, Sankhya: Indian Journal of Statistics 61 (1999) 443.

R. Farebrother, ”Further results on the mean square error of ridge regression”, J R Stat Soc. B38 (1976) 248.

G. Trenkler & H. Toutenburg, ”Mean squared error matrix comparisons between biased estimators-an overview of recent results”, Stat Pap. 31 (1990) 165.

A. F. Lukman & K. Ayinde, ”Review and classifications of the ridge parameter estimation techniques”, Hacettepe Math Stat 46 (2017) 953.

K. Ayinde, A. F. Lukman, O. O. Samuel & S. Ajiboye, ”Some new adjusted ridge estimators of linear regression model”, Int J Civ Eng Technol 9 (2018) 2838.

A. T. Owolabi, K. Ayinde & O. O. Alabi, ”A New Ridge-Type Estimator for the Linear Regression Model with correlated regressors”, Concurrency and Computation: Practice and Experience (2022) CPE6933.

I. Dawoud, A. Lukman & H. Abdul-Rahaman, ”A new biased regression estimator: Theory, simulation, and application”, Scientific African (2022).

G. C. McDonald & D. I. Galarneau, ”A Monte Carlo evaluation of some ridge-type estimators”, Journal of the American Statistical Association 70 (1975) 407.

D. G. Gibbons, ”A simulation study of some ridge estimators”, Journal of the American Statistical Association 76 (1981) 131.

A. F. Lukman, K. Ayinde, S. K. Sek & E. Adewuyi, ”A modified new two-parameter estimator in a linear regression model”, Model. Simul.

Eng. (2019) 1.

L. L. Firinguetti, ”A simulation study of ridge regression estimators with autocorrelated errors”, Communications in Statistics Simulation and Computation 18 (1989) 673.

J. P. Newhouse & S. D. Oman,”An evaluation of ridge estimators”, A report prepared for United States air force project RAND (1971).

H. Woods, H. H. Steinour & Starke, ”E ect of composition of Portland cement on heat evolved during hardening”, Industrial & Engineering Chemistry 24 (1932) 1207.

K. Ayinde, A. F. Lukman, O. O. Samuel & S. A. Ajiboye, ”Some new adjusted ridge estimators of linear regression model”, Int. J. Civ. Eng. Technol. 9 (2018) 2838.

A. F. Lukman, K. Ayinde, S. Binuomote&O. A. Clement, ”Modified ridge-type estimator to combat multicollinearity: application to chemical data”, Journal of Chemometrics 33 (2019b) e3125.

Published

2022-12-29

How to Cite

On the biased Two-Parameter Estimator to Combat Multicollinearity in Linear Regression Model. (2022). African Scientific Reports, 1(3), 188–204. https://doi.org/10.46481/asr.2022.1.3.57

Issue

Volume 1, Issue 3, December 2022

Section

Original Research
Copyright & Licensing

Copyright (c) 2022 Janet Iyabo Idowu, Olasunkanmi James Oladapo, Abiola Timothy Owolabi, Kayode Ayinde

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

On the biased Two-Parameter Estimator to Combat Multicollinearity in Linear Regression Model. (2022). African Scientific Reports, 1(3), 188–204. https://doi.org/10.46481/asr.2022.1.3.57