Year 2023,
Volume: 1 Issue: 2, 74 - 85, 17.12.2023
Kadri Ulaş Akay
Esra Ertan
Ali Erkoç
References
- 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
- 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
- Babar, I., and Chand, S. (2022). Weighted ridge and Liu estimators for linear regression model. Concurrency and Computation: Practice and Experience, e7343. google scholar
- Dawoud, I., Lukman, A. F., Haadi, A. R. (2022). A new biased regression estimator: Theory, simulation and application. Scientific African, 15, e01100. google scholar
- Farebrother, R. W. (1976).Further results on the mean square error of ridge regression. J R Stat Soc B, 28, 248–250. google scholar
- Hoerl A.E., Kennard R.W. (1970).Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67. google scholar
- 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
- 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
- Kibria, B. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics: Simulation and Computation, 32(2), 419–435. google scholar
- 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
- Kurnaz, F. S., Akay, K. U. (2015). A new Liu-type estimator. Stat Papers, 56, 495–517. google scholar
- 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
- Liu, K. (1993). A new class of biased estimate in linear regression. Commun Stat Theory Methods, 22(2), 393–402. google scholar
- 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
- 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
- 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
- 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
- Özkale M.R., Kaçıranlar S. (2007). The restricted and unrestricted two-parameter estimators. Commun Stat Theory Methods 36(10) 2707– 2725. google scholar
- 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
- 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
- Sakallıoğlu S., Kaçıranlar S. (2008). A new biased estimator based on ridge estimation. Stat Pap 49 4178–4196. google scholar
- 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
- 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
- Theobald, C. M. (1974). Generalizations of mean square error applied to ridge regression. J R Stat So B 36 103–106. google scholar
- 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
- 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
- Yang H., Chang X. (2010). A new two-parameter estimator in linear regression. Commun Stat Theory Methods 39(6) 923–934. google scholar
- 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
A New biased estimator and variations based on the Kibria Lukman Estimator
Year 2023,
Volume: 1 Issue: 2, 74 - 85, 17.12.2023
Kadri Ulaş Akay
Esra Ertan
Ali Erkoç
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.
References
- 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
- 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
- Babar, I., and Chand, S. (2022). Weighted ridge and Liu estimators for linear regression model. Concurrency and Computation: Practice and Experience, e7343. google scholar
- Dawoud, I., Lukman, A. F., Haadi, A. R. (2022). A new biased regression estimator: Theory, simulation and application. Scientific African, 15, e01100. google scholar
- Farebrother, R. W. (1976).Further results on the mean square error of ridge regression. J R Stat Soc B, 28, 248–250. google scholar
- Hoerl A.E., Kennard R.W. (1970).Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67. google scholar
- 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
- 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
- Kibria, B. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics: Simulation and Computation, 32(2), 419–435. google scholar
- 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
- Kurnaz, F. S., Akay, K. U. (2015). A new Liu-type estimator. Stat Papers, 56, 495–517. google scholar
- 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
- Liu, K. (1993). A new class of biased estimate in linear regression. Commun Stat Theory Methods, 22(2), 393–402. google scholar
- 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
- 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
- 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
- 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
- Özkale M.R., Kaçıranlar S. (2007). The restricted and unrestricted two-parameter estimators. Commun Stat Theory Methods 36(10) 2707– 2725. google scholar
- 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
- 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
- Sakallıoğlu S., Kaçıranlar S. (2008). A new biased estimator based on ridge estimation. Stat Pap 49 4178–4196. google scholar
- 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
- 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
- Theobald, C. M. (1974). Generalizations of mean square error applied to ridge regression. J R Stat So B 36 103–106. google scholar
- 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
- 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
- Yang H., Chang X. (2010). A new two-parameter estimator in linear regression. Commun Stat Theory Methods 39(6) 923–934. google scholar
- 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