# Inference for monotone single-index conditional means: A Lorenz regression approach

*Cédric Heuchenne* and
*Alexandre Jacquemain*

*Computational Statistics & Data Analysis*, 2022, vol. 167, issue C

**Abstract:**
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.

**Keywords:** Single-index model; Monotone rank estimator; Lorenz curve; Income inequality (search for similar items in EconPapers)

**Date:** 2022

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:csdana:v:167:y:2022:i:c:s016794732100181x

**DOI:** 10.1016/j.csda.2021.107347

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