Estimation nonparamétrique de la distribution des revenus et de l'indice de pauvreté

Galaye Dia

doi:10.1016/j.crma.2008.07.004

Statistique

Estimation nonparamétrique de la distribution des revenus et de l'indice de pauvreté
[Nonparametric estimation of income distribution and poverty index]

Presented by: Paul Deheuvels

Galaye Dia ¹

¹ LERSTAD, UFR de sciences appliquées et de technologie, B.P. 234, Université Gaston-Berger-de-Saint-Louis, Saint-Louis, Sénégal

Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 907-912.

Abstract
Résumé

In this Note we propose an estimator of Foster, Greer and Thorbecke class of measures $P (z, α) = \int_{0}^{z} {(\frac{z - x}{z})}^{α} f (x) d x$ where z is the poverty line, $f (x)$ the density of the income distribution and α the so-called poverty aversion. The estimator is constructed with Parzen–Rosenblatt kernel. Uniform almost sure consistency and uniform mean square consistency are established. A simulation study indicates that this new estimator performs well in finite samples.

Dans cette Note nous proposons un estimateur de l'indice de pauvreté de Foster, Greer et Thorbecke. L'estimateur est construit à l'aide du noyau de Parzen Rosenblatt. La convergence de l'estimateur est étudiée et des simulations proposées.

Received: 2007-06-23
Accepted: 2008-07-03
Published online: 2008-08-01

DOI: 10.1016/j.crma.2008.07.004

Author's affiliations:

Galaye Dia ¹

¹ LERSTAD, UFR de sciences appliquées et de technologie, B.P. 234, Université Gaston-Berger-de-Saint-Louis, Saint-Louis, Sénégal

@article{CRMATH_2008__346_15-16_907_0,
     author = {Galaye Dia},
     title = {Estimation nonparam\'etrique de la distribution des revenus et de l'indice de pauvret\'e},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {907--912},
     publisher = {Elsevier},
     volume = {346},
     number = {15-16},
     year = {2008},
     doi = {10.1016/j.crma.2008.07.004},
     language = {fr},
}

TY  - JOUR
AU  - Galaye Dia
TI  - Estimation nonparamétrique de la distribution des revenus et de l'indice de pauvreté
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 907
EP  - 912
VL  - 346
IS  - 15-16
PB  - Elsevier
DO  - 10.1016/j.crma.2008.07.004
LA  - fr
ID  - CRMATH_2008__346_15-16_907_0
ER  -

%0 Journal Article
%A Galaye Dia
%T Estimation nonparamétrique de la distribution des revenus et de l'indice de pauvreté
%J Comptes Rendus. Mathématique
%D 2008
%P 907-912
%V 346
%N 15-16
%I Elsevier
%R 10.1016/j.crma.2008.07.004
%G fr
%F CRMATH_2008__346_15-16_907_0

Galaye Dia. Estimation nonparamétrique de la distribution des revenus et de l'indice de pauvreté. Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 907-912. doi : 10.1016/j.crma.2008.07.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.07.004/

References
Cited by

[1] J.E. Foster; J. Greer; E. Thorbecke A class of decomposable poverty measures, Econometrica, Volume 52 (1984), pp. 761-776

[2] J. Kiefer On large deviations of the empirical distribution of vector chance variable and law of iterated logarithm, Pacific J. Math., Volume 11 (1961), pp. 143-154

[3] E. Masry Recursive probability density estimation for weakly dependent stationary process, IEEE Trans. Inform. Theory, Volume IT-32 (1986) no. 2, pp. 254-267

[4] E. Parzen On estimation of probability density function and mode, Ann. Math. Statist., Volume 33 (1962), pp. 1065-1076

[5] C. Seidl Poverty measurement: a survey (D. Bös; M. Rose; C. Seidl, eds.), Welfare and Efficiency in Public Economics, Springer-Verlag, Heidelberg, 1988, pp. 71-147

Cited by Sources:

Comments - Policy