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A penalised bootstrap estimation procedure for the explained Gini coefficient

Author

Listed:
  • Jacquemain, Alexandre

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

  • Heuchenne, Cédric

    (Université de Liège)

  • Pircalabelu, Eugen

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

Abstract

The Lorenz regression estimates the explained Gini coefficient, a quantity with a natural application in the measurement of inequality of opportunity. Assuming a single-index model, it corresponds to the Gini coefficient of the conditional expectation of a response given some covariates and it can be estimated without having to estimate the link function. However, it is prone to overestimation when many covariates are included. In this paper, we propose a penalised bootstrap procedure which selects the relevant covariates and produces valid inference for the explained Gini coefficient. The obtained estimator achieves the Oracle property. Numerically, it is computed by the SCAD-FABS algorithm, an adaptation of the FABS algorithm to the SCAD penalty. The performance of the procedure is ensured by theoretical guarantees and assessed via Monte-Carlo simulations. Finally, a real data example is presented.

Suggested Citation

  • 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).
    • Handle: RePEc:aiz:louvad:2024005
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    References listed on IDEAS

    as
    1. François Bourguignon & Francisco H. G. Ferreira & Marta Menéndez, 2007. "Inequality Of Opportunity In Brazil," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(4), pages 585-618, December.
    2. Shi, Xingjie & Huang, Yuan & Huang, Jian & Ma, Shuangge, 2018. "A Forward and Backward Stagewise algorithm for nonconvex loss functions with adaptive Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 235-251.
    3. Heuchenne, Cédric & Jacquemain, Alexandre, 2022. "Inference for monotone single-index conditional means: A Lorenz regression approach," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    4. Francisco H. G. Ferreira & Jérémie Gignoux, 2011. "The Measurement Of Inequality Of Opportunity: Theory And An Application To Latin America," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 57(4), pages 622-657, December.
    5. Lin, Huazhen & Peng, Heng, 2013. "Smoothed rank correlation of the linear transformation regression model," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 615-630.
    6. repec:dau:papers:123456789/1552 is not listed on IDEAS
    7. Juan Carlos Escanciano & Joel Robert Terschuur, 2022. "Machine Learning Inference on Inequality of Opportunity," Papers 2206.05235, arXiv.org, revised Oct 2023.
    8. Francisco H.G. Ferreira & Jérémie Gignoux, 2011. "The Measurement of Inequality of Inequality of Opportunity: Theory and an Application to Latin America," Post-Print halshs-00754503, HAL.
    9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    10. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    11. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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    More about this item

    Keywords

    FABS algorithm ; Gini coefficient ; Lorenz regression ; SCAD penalty ; single-index models;
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