On goodness of fit measures for Gini regression

The semi parametric Gini regression is more robust than ordinary least squares (OLS) regression when the underlying assumptions of the OLS fail and therefore has been used by many researchers. Several measures for goodness of fit of Gini regression were suggested in the literature. However, to the best of our knowledge, these were not compared. We examine the effect of one outlier on several goodness of fit measures in the case of a simple linear regression model via simulation. We base our comparison on the sensitivity curve. As expected, all measures under study are less sensitive to the outlier as the sample size increases. Results indicate that the least sensitive measure to an outlier is Gini correlation between the predictor Y_hat, based on Gini regression, and the observed value Y.