Statistique
Estimation nonparamétrique de la distribution des revenus et de l'indice de pauvreté
[Nonparametric estimation of income distribution and poverty index]
Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 907-912.

In this Note we propose an estimator of Foster, Greer and Thorbecke class of measures P(z,α)=0z(zxz)αf(x)dx 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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.07.004
Dia, Galaye 1

1 LERSTAD, UFR de sciences appliquées et de technologie, B.P. 234, Université Gaston-Berger-de-Saint-Louis, Saint-Louis, Sénégal
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Dia, Galaye. 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. http://www.numdam.org/articles/10.1016/j.crma.2008.07.004/

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

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

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

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

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