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

Author

Listed:
  • Heuchenne, Cédric
  • Jacquemain, Alexandre

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

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- 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.

Suggested Citation

  • Heuchenne, Cédric & Jacquemain, Alexandre, 2021. "Inference for monotone single-index conditional means: A Lorenz regression approach," LIDAM Reprints ISBA 2021043, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2021043
    DOI: https://doi.org/10.1016/j.csda.2021.107347
    Note: In: Computational Statistics & Data Analysis, 2022, vol. 167, 107347
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