Lorenz Model Selection

In the paper, we introduce novel model selection measures based on Lorenz zonoids which, differently from measures based on correlations, are based on a mutual notion of variability and are more robust to the presence of outlying observations. By means of Lorenz zonoids, which in the univariate case correspond to the Gini coefficient, the contribution of each explanatory variable to the predictive power of a linear model can be measured more accurately. Exploiting Lorenz zonoids, we develop a Marginal Gini Contribution measure that allows to measure the absolute explanatory power of any covariate, and a Partial Gini Contribution measure that allows to measure the additional contribution of a new covariate to an existing model.