DefinePK

Abstract

Following Khalaf and Shukur (2005), Alkhamisi et al. (2006) and Muniz et al. (2010), this paper considers several estimators for estimating the Ridge parameter k . This paper differs from aforementioned papers in three ways: 1. the number of regressors considered is between 4 to 12 instead of 2 to 4 which are the usual practice. 2. Both mean square error (MSE) and prediction sum of square (PRESS) are considered as the performance criterion. 3. Different error variances are used (σ is between 0.5 and 5). To compare the performance of the estimators, a simulation study has been conducted. It is evident that increasing the correlation between the independent variables has negative effect on the MSE and PRESS, while 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 remain the same under both the MSE and PRESS criterion. However, the performance of the estimators depends on the amount of error variances specifically, when the sample sizes are small.