A new robust ridge estimator for linear regression model with non normal, heteroscedastic and autocorrelated errors

The ridge regression models the dependent variable as a function of explanatory variables when collinearity exists in the data set. In this study, a new robust estimator is introduced to determine the optimal value of the ridge parameter when a multicollinearity problem emerges with complex behavior of error term. The suggested ridge estimator is a combination of the number of explanatory variables, the standard error of the regression model, and the maximum eigenvalue of the correlation matrix of the explanatory variables. The effectiveness of the suggested new estimator is assessed using extensive Monte Carlo simulations with different distributions of error terms. The simulation findings reveal that the proposed estimator outperforms the ordinary least square (OLS) and popular and closely related ridge estimators regarding minimum mean squared error (MSE). The application of a new estimator is illustrated on two real-life data sets. The results show that the suggested estimator efficiently handles multicollinearity when the error terms are normally distributed, non normally distributed (positively skewed, exponentially decreasing, symmetrical, and heavy-tailed structure), heteroscedastic, and/or autocorrelated.