A Simulation Study of Some Ridge Regression Estimators under Different Distributional Assumptions

Based on the work of Khalaf and Shukur (2005 Khalaf , G. , Shukur , G. ( 2005 ). Choosing ridge parameters for regression problems . Communications in Statistics – Theory and Methods 34 : 1177 – 1182 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Alkhamisi et al. (2006 Alkhamisi , M. , Khalaf , G. , Shukur , G. ( 2006 ). Some modifications for choosing ridge parameters . Communications in Statistics – Theory and Methods 35 : 2005 – 2020 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and Muniz et al. (2010 Muniz , G. , Kibria , B. M. G. , Shukur , G. ( 2010 ). On developing ridge regression parameters: a graphical Investigation. Submitted for Publication . [Google Scholar]), this article considers several estimators for estimating the ridge parameter k. This article differs from aforementioned articles in three ways: (1) Data are generated from Normal, Student's t, and F distributions with appropriate degrees of freedom; (2) The number of regressors considered are from 4–12 instead of 2–4, which are the usual practice; (3) Both mean square error (MSE) and prediction sum of square (PRESS) are considered as the performance criterion. A simulation study has been conducted to compare the performance of the estimators. Based on the simulation study we found that, increasing the correlation between the independent variables has negative effect on the MSE and PRESS. However, increasing the number of regressors has positive effect on MSE and PRESS. When the sample size increases the MSE decreases even when the correlation between the independent variables is large. It is interesting to note that the dominance pictures of the estimators are remained the same under both the MSE and PRESS criterion. However, the performance of the estimators depends on the choice of the assumption of the error distribution of the regression model.