Probability theory/Statistics
Non-parametric estimation of income distribution and poverty index in the unidimensional context with α]0,1[
Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 947-952.

In this paper, we propose an estimator of Foster, Greer and Thorbecke class of measures P(z,α)=0z(zxz)αf(x)dx, where z>0 is the poverty line, f(x) is the density distribution of the income random variable and α]0,1[ is the so-called poverty aversion. α]0,1[ remained an open problem in the work of Dia [1], where he was considering the case where α=0 and α1. The estimator is constructed with the Parzen–Rosenblatt Kernel. Almost sure uniform convergence and uniform convergence in mean square error are established. Finally, the new estimator has been applied to the study of the poverty in Senegal. The study of this application indicates that our new estimator performs well.

Dans cette note, nous proposons un estimateur de l'indice de pauvreté de Foster, Greer et Thorbecke, défini par : P(z,α)=0z(zxz)αf(x)dx, où z>0 est le seuil de pauvreté, f(x) la densité de la distribution des revenus et α]0,1[ est le paramètre d'aversion de la pauvreté. Le cas α]0,1[ restait un cas ouvert dans le travail de Dia [1], où il a considéré les cas α=0 et α1. L'estimateur est construit à l'aide du noyau de Parzen–Rosenblatt. La convergence uniforme presque sûre et la convergence uniforme en erreur quadratique moyenne sont établies. Enfin, notre estimateur a été appliqué à l'étude de la pauvreté au Sénégal. L'étude de cette application montre que notre estimateur est recommandé.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.08.007
Ciss, Youssou 1; Dia, Galaye 1; Diakhaby, Aboubakary 1

1 LERSTAD, UFR de sciences appliquées et de technologie, B P 234, Université Gaston-Berger, Saint-Louis, Senegal
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Ciss, Youssou; Dia, Galaye; Diakhaby, Aboubakary. Non-parametric estimation of income distribution and poverty index in the unidimensional context with $ \alpha \in \phantom{\rule{0.2em}{0ex}}]0,1[$. Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 947-952. doi : 10.1016/j.crma.2015.08.007. http://www.numdam.org/articles/10.1016/j.crma.2015.08.007/

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