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Modelling and Simulation in Engineering
Volume 2019, Article ID 6342702, 10 pages
https://doi.org/10.1155/2019/6342702
Research Article

A Modified New Two-Parameter Estimator in a Linear Regression Model

1Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria
2Department of Statistics, Federal University of Technology, Akure, Nigeria
3School of Mathematical Sciences, Universiti Sains Malaysia, Malaysia

Correspondence should be addressed to Adewale F. Lukman; gn.ude.uml@imnaralof.elaweda

Received 31 December 2018; Revised 25 February 2019; Accepted 5 March 2019; Published 26 May 2019

Academic Editor: Zhiping Qiu

Copyright © 2019 Adewale F. Lukman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The literature has shown that ordinary least squares estimator (OLSE) is not best when the explanatory variables are related, that is, when multicollinearity is present. This estimator becomes unstable and gives a misleading conclusion. In this study, a modified new two-parameter estimator based on prior information for the vector of parameters is proposed to circumvent the problem of multicollinearity. This new estimator includes the special cases of the ordinary least squares estimator (OLSE), the ridge estimator (RRE), the Liu estimator (LE), the modified ridge estimator (MRE), and the modified Liu estimator (MLE). Furthermore, the superiority of the new estimator over OLSE, RRE, LE, MRE, MLE, and the two-parameter estimator proposed by Ozkale and Kaciranlar (2007) was obtained by using the mean squared error matrix criterion. In conclusion, a numerical example and a simulation study were conducted to illustrate the theoretical results.