Are most proposed ridge parameter estimators skewed and do they have any effect on MSE values?

Abstract

Multicollinearity is a common problem in multiple regression that occurs whenever two or more explanatory variables are highly correlated. When multicollinearity exists, the method of Ordinary Least Square (OLS) is likely to produce poor parameter estimates. Furthermore, OLS estimates of regression coefficients can be inflated making them too large. Ridge regression is one of the most popular methods used in the presence of multicollinearity as an alternative. In this study, a comparison of all ridge regression estimators encountered in the literature is conducted in terms of their distributions and Mean Square Error (MSE) values. To this end, 80 different estimators have been studied with comparisons carried out using the Monte Carlo simulations. A distribution was obtained for each ridge parameter and showed, surprisingly, that most are skewed and only a few behave like the Gauss distribution. Interestingly, few of the ridge parameters are distributed within the zero to ten range.