CFP last date
20 October 2025
Call for Paper
November Edition
IJCA solicits high quality original research papers for the upcoming November edition of the journal. The last date of research paper submission is 20 October 2025

Submit your paper
Know more
The week's pick
Responsive image
Zero Trust Architecture Implementation in Enterprise Networks: Evaluating Effectiveness Against Cyber Threats

Stephen Kofi Dotse Samuel Yao Sebuabe Augustus Obeng Silas Asani Abudu Edna Awisie Pappoe
Random Articles
Reseach Article

A Comparative Study of the Performances of the Principal Component Ridge and Principal Component Liu Estimators using Different Forms of Biasing Parameter

by Omokova Mary Attah, Samuel Olayemi Olanrewaju
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 187 - Number 30
Year of Publication: 2025
Authors: Omokova Mary Attah, Samuel Olayemi Olanrewaju
10.5120/ijca2025925518

Omokova Mary Attah, Samuel Olayemi Olanrewaju . A Comparative Study of the Performances of the Principal Component Ridge and Principal Component Liu Estimators using Different Forms of Biasing Parameter. International Journal of Computer Applications. 187, 30 ( Aug 2025), 12-20. DOI=10.5120/ijca2025925518

@article{ 10.5120/ijca2025925518,
author = { Omokova Mary Attah, Samuel Olayemi Olanrewaju },
title = { A Comparative Study of the Performances of the Principal Component Ridge and Principal Component Liu Estimators using Different Forms of Biasing Parameter },
journal = { International Journal of Computer Applications },
issue_date = { Aug 2025 },
volume = { 187 },
number = { 30 },
month = { Aug },
year = { 2025 },
issn = { 0975-8887 },
pages = { 12-20 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume187/number30/a-comparative-study-of-the-performances-of-the-principal-component-ridge-and-principal-component-liu-estimators-using-different-forms-of-biasing-parameter/ },
doi = { 10.5120/ijca2025925518 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2025-08-20T21:35:15.253907+05:30
%A Omokova Mary Attah
%A Samuel Olayemi Olanrewaju
%T A Comparative Study of the Performances of the Principal Component Ridge and Principal Component Liu Estimators using Different Forms of Biasing Parameter
%J International Journal of Computer Applications
%@ 0975-8887
%V 187
%N 30
%P 12-20
%D 2025
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Multicollinearity is a significant issue in multiple linear regression that occurs when two or more independent variables are highly correlated. This correlation undermines the reliability and stability of regression estimates, making it challenging to isolate and interpret the individual effect of each predictor variable. In the presence of multicollinearity, traditional estimation methods like Ordinary Least Squares (OLS) become less effective, often resulting in inflated standard errors and less reliable statistical inference. When multicollinearity exists, biased estimation techniques such as Ridge regression, the Liu estimator, and Principal Component-based estimators are frequently used. These estimators provide more stable and interpretable results when independent variables are correlated. Other estimators that are a combination of existing estimators have been formed. These include the Principal Component Ridge (PCRE) and Principal Component Liu (PCLIU) estimators. They further mitigate the adverse effects of multicollinearity. This study evaluates the performance of PCRE and PCLIU estimators under varying degrees of multicollinearity, sample sizes, and error variances. Seven distinct forms of the biasing parameter k, along with their generalized versions, are examined in this analysis. Originally introduced in 2019 by Fayose and Ayinde, these forms include the maximum, minimum, arithmetic mean, geometric mean, harmonic mean, mid-range, and median. Monte Carlo simulations, repeated 1,000 times, were conducted on regression models with four and seven predictors, across five levels of multicollinearity, three error variances, and eight sample sizes. The Mean Square Error (MSE) criterion was used for evaluation. Results indicate that the maximum form of the Principal Component Ridge estimator consistently outperforms others in terms of efficiency.

References
  1. Gujarati, D. N. (2021). Essentials of econometrics. Sage Publications.
  2. Kibria, B. G., & Lukman, A. F. (2020). A new ridge‐type estimator for the linear regression model: simulations and applications. Scientifica, 2020(1), 9758378.
  3. Paul, R. K. (2006). Multicollinearity: Causes, effects and remedies. IASRI, New Delhi, 1(1), 58–65.
  4. Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis. John Wiley & Sons.
  5. Khalaf, G., & Iguernane, M. (2016). Multicollinearity and a ridge parameter estimation approach. Journal of Modern Applied Statistical Methods, 15(2), 25. https://doi.org/10.22237/jmasm/1478002980
  6. Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67. https://doi.org/10.1080/00401706.1970.10488634
  7. Liu, K. (1993). A new class of biased estimate in linear regression. Communications in Statistics - Theory and Methods, 22(2), 393–402.
  8. Muniz, G., & Kibria, B. M. G. (2009). On Some Ridge Regression Estimators: An Empirical Comparisons. Communications in Statistics - Simulation and Computation, 38(3), 621–630. https://doi.org/10.1080/03610910802592838
  9. Hoerl, A. E., Kannard, R. W., & Baldwin, K. F. (1975). Ridge regression: some simulations. Communications in Statistics, 4(2), 105–123. https://doi.org/10.1080/03610927508827232
  10. McDonald, G. C., & Galarneau, D. I. (1975). A Monte Carlo Evaluation of Some Ridge-Type Estimators. Journal of the American Statistical Association, 70(350), 407–416. https://doi.org/10.1080/01621459.1975.10479882
  11. Lawless F., and Wang P., (1976). A simulation study of ridge and other regression estimators. Communications in Statistics-Theory and Methods 5, p.307-323.
  12. Dempster, A. P., Schatzoff, M., & Wermuth, N. (1977). A Simulation Study of Alternatives to Ordinary Least Squares. Journal of the American Statistical Association, 72(357), 77–91. https://doi.org/10.1080/01621459.1977.10479910
  13. Troskie, CG* & Chalton, DO. "A Bayesian estimate for the constants in ridge regression." South African Statistical Journal 30, no. 2 (1996): 119-137.
  14. Firinguetti, L. (1999). A generalized ridge regression estimator and its finite sample properties: A generalized ridge regression estimator. Communications in Statistics - Theory and Methods, 28(5), 1217–1229. https://doi.org/10.1080/03610929908832353
  15. Kibria, B. M. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics - Simulation and Computation, 32(2), 419–435. https://doi.org/10.1081/SAC-120017499
  16. Khalaf, G., & Shukur, G. (2005). Choosing Ridge Parameter for Regression Problems. Communications in Statistics - Theory and Methods, 34(5), 1177–1182. https://doi.org/10.1081/STA-200056836
  17. Batah, F. S. M., Ramanathan, T. V., & Gore, S. D. (2008). The efficiency of modified jackknife and ridge type regression estimators: a comparison. Surveys in Mathematics and its Applications, 3, 111-122.
  18. Kibria, B. G., & Banik, S. (2016). Some ridge regression estimators and their performances. Journal of Modern Applied statistical methods, 15, 206-238.
  19. Lukman, A. F., & Ayinde, K. (2017). Review and classifications of the ridge parameter estimation techniques. Hacettepe Journal of Mathematics and Statistics, 46(5), 953-967.
  20. Lukman, A. F., Ayinde, K., Oludoun, O., & Onate, C. A. (2020). Combining modified ridge-type and principal component regression estimators. Scientific African, 9, e00536.
  21. Fayose, T. S., & Ayinde, K. (2019). Different forms biasing parameter for generalized ridge regression estimator. International Journal of Computer Applications, 181(37), 2-29.
  22. Baye, M. R., & Parker, D. F. (1984). Combining ridge and principal component regression:a money demand illustration. Communications in Statistics - Theory and Methods, 13(2), 197–205. https://doi.org/10.1080/03610928408828675
  23. Nomura, M., & Ohkubo, T. (1985). A note on combining ridge and principal component regression. Communications in Statistics - Theory and Methods, 14(10), 2489–2493. https://doi.org/10.1080/0361092850882905
  24. Sarkar, N. (1996). Mean square error matrix comparison of some estimators in linear regressions with multicollinearity. Statist. Probab. Lett. 30:133–138.
  25. Kaçıranlar, S., & Sakallıoğlu, S. (2001). Combining the Liu Estimator and The Principal Component Regression Estimator. Communications in Statistics - Theory and Methods, 30(12), 2699–2705. https://doi.org/10.1081/STA-100108454
  26. Ozkale, M. R., & Kaciranlar, S. (2007). Comparisons of the unbiased ridge estimation to the other estimations. Communications in Statistics Theory and Methods, 36(4), 707.
  27. Batah, F. Sh. M., Özkale, M. R., & Gore, S. D. (2009). Combining Unbiased Ridge and Principal Component Regression Estimators. Communications in Statistics - Theory and Methods, 38(13), 2201–2209. https://doi.org/10.1080/03610920802503396
  28. Crouse, R. H., Chun Jin, & Hanumara, R. C. (1995). Unbiased ridge estimation with prior information and ridge trace. Communications in Statistics - Theory and Methods, 24(9), 2341–2354. https://doi.org/10.1080/03610929508831620
  29. Adegoke, A. S., Adewuyi, E., Ayinde, K., & Lukman, A. F. (2016). A comparative study of some robust ridge and liu estimators. Science World Journal, 11(4), 16-20.
  30. Huang, D., Huang, J., & Bai, D. (2023). Combination of the modified Kibria–Lukman and the principal component regression estimators. Communications in Statistics - Simulation and Computation, 1–16. https://doi.org/10.1080/03610918.2023.2292970
  31. Özbey, F., & Kaçiranlar, S. (2015). Evaluation of the predictive performance of the Liu estimator. Communications in Statistics-Theory and Methods, 44(10), 1981-1993.
  32. Lukman, A. F., Haadi, A., Ayinde, K., Onate, C. A., Gbadamosi, B., & Oladejo, N. K. (2018). Some improved generalized ridge estimators and their comparison. WSEAS Transactions on Mathematics, 17, 369–376.
  33. Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24(6), 417–441. https://doi.org/10.1037/h0071325
  34. Pongpiachan, S., Wang, Q., Apiratikul, R., Tipmanee, D., Li, L., Xing, L., ... & Poshyachinda, S. (2024). Combined use of principal component analysis/multiple linear regression analysis and artificial neural network to assess the impact of meteorological parameters on fluctuation of selected PM2.5-bound elements. Plos one, 19(3), e0287187.
  35. Weeraratne, N., Hunt, L., & Kurz, J. (2024). Challenges of principal component analysis in high-dimensional settings when n < p. Preprint. https://doi.org/10.21203/rs.3.rs-4033858/v1
  36. Ayinde, K., Apata, E. O., & Alaba, O. O. (2012). Estimators of linear regression model and prediction under some assumptions violation. https://doi.org/ 10.4236/ojs.2012.25069
  37. Wichern, D. W., & Churchill, G. A. (1978). A comparison of ridge estimators. Technometrics, 20(3), 301–311. https://doi.org/10.1080/00401706.1978.10489675
  38. Gibbons, D. G. (1981). A simulation study of some ridge estimators. Journal of the American Statistical Association, 76(373), 131-139
  39. Dorugade, A. V., & Kashid, D. N. (2010). Alternative method for choosing ridge parameter for regression. Applied Mathematical Sciences, 4(9), 447–456
  40. Dorugade, A. V. (2016). Adjusted ridge estimator and comparison with Kibria’s method in linear regression. Journal of the Association of Arab Universities for Basic and Applied Sciences, 21, 96–102.
  41. Amalare, A. A., Ayinde, K., & Onanuga, K. (2023). Parameter Estimation of Linear Regression Model with Multicollinearity and Heteroscedasticity Problems. The Journals of the Nigerian Association of Mathematical Physics, 65, 207-216.
Index Terms

Computer Science
Information Sciences

Keywords

Ordinary Least Squares Ridge Regression Estimator Liu Estimator Principal Component Estimator Principal Component Ridge Estimator Principal Component Liu Estimator.

Powered by PhDFocusTM