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.
Funding Statement
Computational resources have been provided by the supercomputing facilities of the UCLouvain (CISM/UCL) and the Consortium des Équipements de Calcul Intensif en Fédération Wallonie Bruxelles (CÉCI) funded by the Fond de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under convention 2.5020.11.
Acknowledgments
The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.
Citation
Alexandre Jacquemain. Cédric Heuchenne. Eugen Pircalabelu. "A penalised bootstrap estimation procedure for the explained Gini coefficient." Electron. J. Statist. 18 (1) 247 - 300, 2024. https://doi.org/10.1214/23-EJS2200
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