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

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  • Heuchenne, Cédric
  • Jacquemain, Alexandre

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.

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  • Heuchenne, Cédric & Jacquemain, Alexandre, 2022. "Inference for monotone single-index conditional means: A Lorenz regression approach," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:csdana:v:167:y:2022:i:c:s016794732100181x
    DOI: 10.1016/j.csda.2021.107347
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    1. Jacquemain, Alexandre & Heuchenne, Cédric & Pircalabelu, Eugen, 2024. "A penalised bootstrap estimation procedure for the explained Gini coefficient," LIDAM Discussion Papers ISBA 2024005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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