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

Tuğba Söküt Açar

doi:10.53570/jnt.1139885

EN

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

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

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Details

Primary Language

English

Subjects

Applied Mathematics

Journal Section

Research Article

Authors

Tuğba Söküt Açar ^*
0000-0002-4444-1671
Türkiye

Publication Date

December 31, 2022

Submission Date

July 4, 2022

Acceptance Date

November 11, 2022

Published in Issue

Year 2022 Number: 41

DOI

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

IZ

https://izlik.org/JA57DC24UZ

APA

Söküt Açar, T. (2022). Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation. Journal of New Theory, 41, 1-17. https://doi.org/10.53570/jnt.1139885

AMA

1.Söküt Açar T. Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation. JNT. 2022;(41):1-17. doi:10.53570/jnt.1139885

Chicago

Söküt Açar, Tuğba. 2022. “Kibria-Lukman Estimator for General Linear Regression Model With AR(2) Errors: A Comparative Study With Monte Carlo Simulation”. Journal of New Theory, nos. 41: 1-17. https://doi.org/10.53570/jnt.1139885.

EndNote

Söküt Açar T (December 1, 2022) Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation. Journal of New Theory 41 1–17.

IEEE

[1]T. Söküt Açar, “Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation”, JNT, no. 41, pp. 1–17, Dec. 2022, doi: 10.53570/jnt.1139885.

ISNAD

Söküt Açar, Tuğba. “Kibria-Lukman Estimator for General Linear Regression Model With AR(2) Errors: A Comparative Study With Monte Carlo Simulation”. Journal of New Theory. 41 (December 1, 2022): 1-17. https://doi.org/10.53570/jnt.1139885.

JAMA

1.Söküt Açar T. Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation. JNT. 2022;:1–17.

MLA

Söküt Açar, Tuğba. “Kibria-Lukman Estimator for General Linear Regression Model With AR(2) Errors: A Comparative Study With Monte Carlo Simulation”. Journal of New Theory, no. 41, Dec. 2022, pp. 1-17, doi:10.53570/jnt.1139885.

Vancouver

1.Tuğba Söküt Açar. Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation. JNT. 2022 Dec. 1;(41):1-17. doi:10.53570/jnt.1139885