SavedAdd your journal

Journals / Istanbul Journal of Mathematics / 2023 / Volume: 1 Issue: 2

A New biased estimator and variations based on the Kibria Lukman Estimator

Kadri Ulaş Akay(Istanbul University, Faculty of Science, Department of Mathematics)0000-0002-8668-2879
Esra Ertan(Istanbul University, Faculty of Science, Department of Mathematics)0000-0002-6020-8749
Ali Erkoç(Mimar Sinan Fine Arts University, Faculty of Arts and Sciences, Department of Statistics)0000-0003-4597-4282
Pages
—
Publication Date
2023-12-17
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A numerical example is given to evaluate the performance of the proposed estimator against other biased estimators.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:One of the problems encountered in linear regression models is called multicollinearity problem which is an approximately linear relationship between the explanatory variables.
📊
Key Findings & Data:In addition, two different Monte Carlo simulation experiments are carried out to examine the performance of the biased estimators under consideration.
💡
Conclusion & Impact:A numerical example is given to evaluate the performance of the proposed estimator against other biased estimators.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Liu estimator · Liu-type estimator · multicollinearity

Abstract

One of the problems encountered in linear regression models is called multicollinearity problem which is an approximately linear relationship between the explanatory variables. This problem causes the estimated parameter values to be highly sensitive to small changes in the data. In order to reduce the impact of this problem on the model parameters, alternative biased estimators to the ordinary least squares estimator have been proposed in the literature. In this study, we propose a new biased estimator that can be an alternative to existing estimators. The superiority of this estimator over other biased estimators is analyzed in terms of matrix mean squared error. In addition, two different Monte Carlo simulation experiments are carried out to examine the performance of the biased estimators under consideration. A numerical example is given to evaluate the performance of the proposed estimator against other biased estimators.

🔖

Cite This Article

Akay, K. U., Ertan, E., Erkoç, A. (2023). A New biased estimator and variations based on the Kibria Lukman Estimator. Istanbul Journal of Mathematics, Volume: 1 Issue: 2. https://ajindex.com/articles/1645570

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (28)

  1. Ahmad, S., and Aslam, M. (2022). Another proposal about the new two-parameter estimator for linear regression model with correlated regressors. Communications in Statistics-Simulation and Computation, 51(6), 3054–3072. google scholar
  2. Aslam, M., and Ahmad, S. (2022). The modified Liu-ridge-type estimator: a new class of biased estimators to address multicollinearity. Communications in Statistics-Simulation and Computation, 51(11), 6591–6609. google scholar
  3. Babar, I., and Chand, S. (2022). Weighted ridge and Liu estimators for linear regression model. Concurrency and Computation: Practice and Experience, e7343. google scholar
  4. Dawoud, I., Lukman, A. F., Haadi, A. R. (2022). A new biased regression estimator: Theory, simulation and application. Scientific African, 15, e01100. google scholar
  5. Farebrother, R. W. (1976).Further results on the mean square error of ridge regression. J R Stat Soc B, 28, 248–250. google scholar
  6. Hoerl A.E., Kennard R.W. (1970).Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67. google scholar
  7. Huang, J., Yang, H. (2014).A two-parameter estimator in the negative binomial regression model. Journal of Statistical Computation and Simulation, 84(1), 124–134. google scholar
  8. Idowu, J. I., Oladapo, O. J., Owolabi, A. T., Ayinde, K., Akinmoju, O. (2023). Combating Multicollinearity: A New Two-Parameter Approach. Nicel Bilimler Dergisi, 5(1): 90–100. google scholar
  9. Kibria, B. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics: Simulation and Computation, 32(2), 419–435. google scholar
  10. Kibria, G. B. M. and A. F. Lukman. (2020). A new ridge-type estimator for the linear regression model: Simulations and applications. Scientifica, 2020:9758378. doi:10.1155/2020/9758378. google scholar
  11. Kurnaz, F. S., Akay, K. U. (2015). A new Liu-type estimator. Stat Papers, 56, 495–517. google scholar
  12. Kurnaz, F. S., Akay, K. U. (2018). Matrix mean squared error comparisons of some biased estimators with two biasing parameters. Commun Stat Theory Methods, 47(8), 2022–2035. google scholar
  13. Liu, K. (1993). A new class of biased estimate in linear regression. Commun Stat Theory Methods, 22(2), 393–402. google scholar
  14. Liu, K. (1993). A new class of biased estimate in linear regression. Commun Stat Theory Methods, 22(2), 393–402. Liu, K. (2003). Using Liu-type estimator to combat collinearity. Commun Stat Theory Methods, 32(5), 1009–1020. google scholar
  15. Lukman, A. F., Ayinde, K., Siok Kun, S., & Adewuyi, E. T. (2019). A modified new two-parameter estimator in a linear regression model. Modelling and Simulation in Engineering. vol. 2019, Article ID 6342702. google scholar
  16. Lukman, A. F., Kibria, B. G., Ayinde, K., & Jegede, S. L. (2020). Modified one-parameter Liu estimator for the linear regression model. Modelling and Simulation in Engineering, 2020:1-17. google scholar
  17. McDonald G.C., Galarneau D.I. (1975). A Monte Carlo evaluation of some ridge-type estimators. J Am Stat Assoc 70(350):407–416. google scholar
  18. Özkale M.R., Kaçıranlar S. (2007). The restricted and unrestricted two-parameter estimators. Commun Stat Theory Methods 36(10) 2707– 2725. google scholar
  19. Qasim, M., Amin, M., Omer, T. (2020). Performance of some new Liu parameters for the linear regression model. Communications in Statistics-Theory and Methods 49(17) 4178–4196. google scholar
  20. Qasim, M., Månsson, K., Sjölander, P., Kibria, B. G. (2022). A new class of efficient and debiased two-step shrinkage estimators: method and application. Journal of Applied Statistics, 49(16) 4181–4205. google scholar
  21. Sakallıoğlu S., Kaçıranlar S. (2008). A new biased estimator based on ridge estimation. Stat Pap 49 4178–4196. google scholar
  22. Shewa G. A. and Ugwuowo F. I. (2023). A new hybrid estimator for linear regression model analysis: Computations and simulations. Scientific African, 19 e01441. google scholar
  23. Stein C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution, vol. 1. In “Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability", 197–206. google scholar
  24. Theobald, C. M. (1974). Generalizations of mean square error applied to ridge regression. J R Stat So B 36 103–106. google scholar
  25. Trenkler G., Toutenburg H. (1990). Mean squared error matrix comparisons between biased estimator- an overview of recent results. Stat Pap 31 165–179. google scholar
  26. Üstündağ Ş. G., Toker, S., Özbay, N. (2021). Defining a two-parameter estimator: a mathematical programming evidence. Journal of Statistical Comput. and Simul. 91(11) 2133–2152. google scholar
  27. Yang H., Chang X. (2010). A new two-parameter estimator in linear regression. Commun Stat Theory Methods 39(6) 923–934. google scholar
  28. Zeinal, A., and Azmoun Zavie Kivi, M. R. (2023). The generalized new two-type parameter estimator in linear regression model. Comm. Statist. Simulation Comput. 52(1) 98–109. google scholar