Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation

Year 2022, Issue: 41, 1 - 17, 31.12.2022

Tuğba Söküt Açar

https://doi.org/10.53570/jnt.1139885

Abstract

The sensitivity of the least-squares estimation in a regression model is impacted by multicollinearity and autocorrelation problems. To deal with the multicollinearity, Ridge, Liu, and Ridge-type biased estimators have been presented in the statistical literature. The recently proposed Kibria-Lukman estimator is one of the Ridge-type estimators. The literature has compared the Kibria-Lukman estimator with the others using the mean square error criterion for the linear regression model. It was achieved in a study conducted on the Kibria-Lukman estimator's performance under the first-order autoregressive erroneous autocorrelation. When there is an autocorrelation problem with the second-order, evaluating the performance of the Kibria-Lukman estimator according to the mean square error criterion makes this paper original. The scalar mean square error of the Kibria-Lukman estimator under the second-order autoregressive error structure was evaluated using a Monte Carlo simulation and two real examples, and compared with the Generalized Least-squares, Ridge, and Liu estimators.
The findings revealed that when the variance of the model was small, the mean square error of the Kibria-Lukman estimator gave very close values with the popular biased estimators. As the model variance grew, Kibria-Lukman did not give fairly similar values with popular biased estimators as in the model with small variance. However, according to the mean square error criterion the Kibria-Lukman estimator outperformed the Generalized Least-Squares estimator in all possible cases.

Keywords

Autocorrelation, multicollinearity, second-order autoregressive errors, Kibria-Lukman estimator

References

• D. A. Belsley, E. Kuh, R. E. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, John Wiley & Sons, New Jersey, 2005.
• A. E. Hoerl, R. W. Kennard, Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics 12 (1) (1970) 55–67.
• A. E. Hoerl, R. W. Kannard, K. F. Baldwin, Ridge Regression: Some Simulations, Communications in Statistics-Theory and Methods 4 (2) (1975) 105–123.
• L. JF, A Simulation Study of Ridge and Other Regression Estimators, Communications in Statistics-Theory and Methods 5 (4) (1976) 307–323.
• K. Liu, Using Liu-Type Estimator to Combat Collinearity, Communications in Statistics-Theory and Methods 32 (5) (2003) 1009–1020.
• K. Liu, A New Class of Blased Estimate in Linear Regression, Communications in Statistics-Theory and Methods 22 (2) (1993) 393–402.
• M. R. Özkale, S. Kaçıranlar, A Prediction-Oriented Criterion for Choosing the Biasing Parameter in Liu Estimation, Communications in Statistics-Theory and Methods 36 (10) (2007) 1889–1903.
• S. Kaçıranlar, S. Sakallıoğlu, Combining the Liu Estimator and the Principal Component Regression Estimator, Communications in Statistics-Theory and Methods 30 (12) (2001) 2699–2705.
• G. B. Kibria, A. F. Lukman, A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications, Scientifica Article ID 9758378 (2020) 16 pages.
• M. R. Özkale, S. Kaçıranlar, The Restricted and Unrestricted Two-Parameter Estimators, Communications in Statistics-Theory and Methods 36 (15) (2007) 2707–2725.
• A. F. Lukman, Z. Y. Algamal, B. G. Kibria, K. Ayinde, The KL Estimator for the Inverse Gaussian Regression Model, Concurrency and Computation: Practice and Experience 33 (13) (2021) e6222.
• A. F. Lukman, G. B. Kibria, Almon-KL Estimator for the Distributed Lag Model, Arab Journal of Basic and Applied Sciences 28 (1) (2021) 406–412.
• A. F. Lukman, I. Dawoud, B. Kibria, Z. Y. Algamal, B. Aladeitan, A New Ridge-Type Estimator for the Gamma Regression Model, Scientifica 2021.
• H. E. Oranye, F. I. Ugwuowo, Modified Jackknife Kibria–Lukman Estimator for the Poisson Regression Model, Concurrency and Computation: Practice and Experience 34 (6) (2022) e6757.
• A. A. Hamad, Z. Y. Algamal, Jackknifing KL estimator in Poisson Regression Model, Periodicals of Engineering and Natural Sciences (PEN) 10 (2) (2022) 314–322.
• G. Trenkler, On the Performance of Biased Estimators in the Linear Regression Model with Correlated or Heteroscedastic Errors, Journal of Econometrics 25 (1-2) (1984) 179–190.
• S. Kaçıranlar, Liu Estimator in the General Linear Regression Model, Journal of Applied Statistical Science 13 (2003) 229–234.
• G. Judge, R. Hill, W. Griffiths, H. Lutkepohl, T. Lee, Introduction to the Theory and Practice of Econometrics, Wiley, New Jersey, 1988.
• S. S. Roy, S. Guria, Regression Diagnostics in an Autocorrelated Model, Brazilian Journal of Probability and Statistics 18 (2) (2004) 103–112.
• H. Vinod, A. Ullah, Recent Advances in Regression Methods, Marcel Dekker, New York, 1981.
• G. G. Judge, W. Griffiths, R. Hill, H. Lutkepohl, T. Lee, The Theory and Practice of Econometrics, John Wiley & Sons, New York, 1985.
• M. A. Zubair, M. O. Adenomon, Comparison of Estimators Efficiency for Linear Regressions with Joint Presence of Autocorrelation and Multicollinearity, Science World Journal 16 (2) (2021) 103–109.
• H. Yang, X. Chang, A New Two-Parameter Estimator in Linear Regression, Communications in Statistics-Theory and Methods 39 (6) (2010) 923–934.
• G. C. McDonald, D. I. Galarneau, A Monte Carlo Evaluation of Some Ridge-Type Estimators, Journal of the American Statistical Association 70 (350) (1975) 407–416.
• B. G. Kibria, Performance of Some New Ridge Regression Estimators, Communications in Statistics-Simulation and Computation 32 (2) (2003) 419–435.
• E. Malinvard, Statistical: Methods of Econometrics, North Holland, Amsterdam, 1980.
• F. I. Ugwuowo, H. E. Oranye, K. C. Arum, On the Jackknife Kibria-Lukman Estimator for the Linear Regression Model, Communications in Statistics-Simulation and Computation (2021) 1–13.