A penalised bootstrap estimation procedure for the explained Gini coefficient

Alexandre Jacquemain (), Cédric Heuchenne () and Eugen Pircalabelu ()
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Alexandre Jacquemain: Université catholique de Louvain, LIDAM/ISBA, Belgium
Cédric Heuchenne: Université de Liège
Eugen Pircalabelu: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2024005, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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.

Keywords: FABS algorithm; Gini coefficient; Lorenz regression; SCAD penalty; single-index models (search for similar items in EconPapers)
Pages: 54
Date: 2024-02-13
Note: In : Electronic Journal of Statistics, 2024, vol. 18(1), p. 247-300
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2024005

DOI: 10.1214/23-EJS2200

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