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.

中文翻译：

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洛伦兹模型选择

在这篇论文中，我们介绍了基于洛伦兹环带的新模型选择度量，与基于相关性的度量不同，它基于可变性的相互概念，并且对外围观察的存在更加稳健。通过洛伦兹环带（在单变量情况下对应于基尼系数），可以更准确地测量每个解释变量对线性模型预测能力的贡献。利用 Lorenz zonoids，我们开发了一个边际基尼贡献度量，允许测量任何协变量的绝对解释能力，以及一个部分基尼贡献度量，允许测量新协变量对现有模型的额外贡献。