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

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...

Full description

Saved in:
Bibliographic Details
Main Author: Tuğba Söküt Açar
Format: Article
Language:English
Published: Naim Çağman 2022-12-01
Series:Journal of New Theory
Subjects:
Online Access:https://dergipark.org.tr/en/download/article-file/2522684
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850079848275378176
author Tuğba Söküt Açar
author_facet Tuğba Söküt Açar
author_sort Tuğba Söküt Açar
collection DOAJ
description 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.
format Article
id doaj-art-cf06de53741d44788bb480e3cd46461d
institution DOAJ
issn 2149-1402
language English
publishDate 2022-12-01
publisher Naim Çağman
record_format Article
series Journal of New Theory
spelling doaj-art-cf06de53741d44788bb480e3cd46461d2025-08-20T02:45:06ZengNaim ÇağmanJournal of New Theory2149-14022022-12-014111710.53570/jnt.11398852425Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo SimulationTuğba Söküt Açar0https://orcid.org/0000-0002-4444-1671Çanakkale Onsekiz Mart ÜniversitesiThe 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.https://dergipark.org.tr/en/download/article-file/2522684autocorrelationmulticollinearitysecond-order autoregressive errorskibria-lukman estimator
spellingShingle Tuğba Söküt Açar
Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation
Journal of New Theory
autocorrelation
multicollinearity
second-order autoregressive errors
kibria-lukman estimator
title Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation
title_full Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation
title_fullStr Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation
title_full_unstemmed Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation
title_short Kibria-Lukman Estimator for General Linear Regression Model with AR(2) Errors: A Comparative Study with Monte Carlo Simulation
title_sort kibria lukman estimator for general linear regression model with ar 2 errors a comparative study with monte carlo simulation
topic autocorrelation
multicollinearity
second-order autoregressive errors
kibria-lukman estimator
url https://dergipark.org.tr/en/download/article-file/2522684
work_keys_str_mv AT tugbasokutacar kibrialukmanestimatorforgenerallinearregressionmodelwithar2errorsacomparativestudywithmontecarlosimulation