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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 Reprints ISBA 2024005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2024005
    DOI: https://doi.org/10.1214/23-EJS2200
    Note: In : Electronic Journal of Statistics, 2024, vol. 18(1), p. 247-300
    as

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