Applied Mathematical Sciences, Vol. 7, 2013, no. 50, 2469 - 2480
HIKARI Ltd, www.m-hikari.com
Ridge Regression Estimators with the Problem
of Multicollinearity
Maie M. Kamel
Statistic Department, Faculty of Commerce
Tanta Univeristy, Tanta, Egypt
maie.m.kamel@gmail.com
Sarah F. Aboud
Egyptian Academy of Computers,
Information & Management Technology
Ministry of High Education, Tanta, Egypt
Sara_aboud@yahoo.com
Copyright © 2013 Maie M. Kamel and Sarah F. Aboud. 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 study aims to illustrate the negative effect of the Multicollinearity problem upon the
specimen, identify the way of Ridge Regression as a way to deal with the Multicollinearity
problem, focus on some of the estimators of Ridge regression as (James and Stein,
Bhattacharya, Heuristic) and identify which estimator from the previously mentioned
estimators is highly preferable to be used, to estimate the parameters of a model which
faces the Multicollinearity problem. Minimum mean-square error (MSE) has been used
as the best measure for estimator. Application has been done on specific data for return on
total assets of a bank after making sure that this data faces the Multicollinearity problem.
Also, simulation method was used to generate fabricated data sets, which gave more space
in the application. According to the study we can see that James and Stein’s estimator has
got the minimum mean square error (MSE). Consequently the study recommends its usage
to estimate model parameters which face the Multicollinearity problem.