Model selection based on Lorenz zonoids

During the last years, the dependence analysis context has assumed a relevant role both in economical and statistical applications. In this paper we focus the attention on the Lorenz zonoid tool: when considering only the univariate case, the Lorenz zonoid corresponds to the Gini measure. Our aim is extending the Lorenz zonoid application to the model selection context. In particular we consider the Lorenz zonoid of a linear regression function characterized by k explanatory variables and we define the partial contribution due to the introduction of a (k+1) explanatory variable. This leads to the definition of a new dependence measure that we call “Relative Gini Index” (RGI).