A Comparison of Different Ridge Parameters under Both Multicollinearity and Heteroscedasticity

Abstract

One of the major problems in fitting an appropriate linear regression model is multicollinearity which occurs when regressors are highly correlated. To overcome this problem, ridge regression estimator which is an alternative method to the ordinary least squares (OLS) estimator, has been used. Heteroscedasticity, which violates the assumption of constant variances, is another major problem in regression estimation. To solve this violation problem, weighted least squares estimation is used to fit a more robust linear regression equation. However, when there is both multicollinearity and heteroscedasticity problem, weighted ridge regression estimation should be employed. Ridge regression depends on the ridge parameter which does not have an explicit form of calculation. There are various ridge parameters proposed in the literature. A simulation study was conducted to compare the performances of these ridge parameters for both multicollinear and heteroscedastic data. The following factors were varied: the number of regressors, sample sizes and degrees of multicollinearity. The performances of the parameters were compared using mean square error. The study also shows that when the data are both heteroscedastic and multicollinear, the estimation performances of the ridge parameters differs from the case for only multicollinear data.