FABS algorithm; Gini coefficient; Lorenz regression; SCAD penalty; single-index models; Statistics and Probability; Statistics, Probability and Uncertainty
Abstract :
[en] 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.
Disciplines :
Quantitative methods in economics & management
Author, co-author :
Jacquemain, Alexandre ; ISBA, UCLouvain, Belgium
Heuchenne, Cédric ; Université de Liège - ULiège > HEC Liège : UER > UER Opérations : Statistique appliquée à la gestion et à l'économie
Pircalabelu, Eugen; HEC Liege, University of Liège, Belgium
Language :
English
Title :
A penalised bootstrap estimation procedure for the explained Gini coefficient
Publication date :
2024
Journal title :
Electronic Journal of Statistics
eISSN :
1935-7524
Publisher :
Institute of Mathematical Statistics
Volume :
18
Issue :
1
Pages :
247 - 300
Peer reviewed :
Peer Reviewed verified by ORBi
Funding text :
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.
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