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The Lorenz regression procedure quantifies the inequality of a response explained by a set of covariates. Formally, it gives a weight to each covariate to maximize the concentration index between the response and a weighted average of the covariates. The obtained index is called the explained Gini coefficient. Unlike methods based on decompositions of inequality measures, the procedure does not assume a linear relationship between the response and the covariates. Inference can be performed by noticing a similarity with the monotone rank estimator, introduced in the context of the single-index model. A continuity correction is presented in the presence of discrete covariates. The Lorenz-R2 is a goodness-of-fit measure evaluating the proportion of explained inequality and is used to build a test of joint significance of several covariates. Monte-Carlo simulations and a real-data example are presented.
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Heuchenne, C., & Jacquemain, A. (2021). Inference for monotone single-index conditional means: a Lorenz regression approach (LIDAM Discussion Paper ISBA 2021/42). https://hdl.handle.net/2078.5/103394