Asymptotic normality of non-parametric estimator for the FGT poverty index via adaptive kernel. (English. French summary) Zbl 1441.62597

Summary: In this paper, we study the kernel estimator of the measurement class of J. Foster et al. [Econometrica 52, 761–766 (1984; Zbl 0555.90029)] to establish the asymptotic normality of the kernel estimator of the FGT poverty index by the adaptive method for the values of \(\alpha = 0\) and \(\alpha \geq 1\). We then provide a performance study of this estimator, on simulated data, compared to the estimator from the non-adaptive kernel and the empirical estimator. The study shows that an adaptive kernel estimator is recommended.


62P20 Applications of statistics to economics
62G07 Density estimation
62E20 Asymptotic distribution theory in statistics
91B82 Statistical methods; economic indices and measures


Zbl 0555.90029
Full Text: Euclid


[1] Ciss Youssou and Diakhaby Aboubakary, 2016. Asymptotic Normality of Non-parametric Estimator for the FGT Poverty Index with when the parameter is strictly between0and 1.Afr. Stat., 11(2), 965-981. · Zbl 1356.60033
[2] Ciss Y., Dia G. and Diakhaby A., 2015. Non-parametric estimation of income distribution and poverty index in the unidimensional context withα∈]0,1[.Comptes Rendus Math ´ematique, 353:10, 947-952. · Zbl 1329.91107
[3] Dia, G., 2009. Asymptotic normality of the kernel poverty measure estimate.Journal of Mathematical Sciences: Advances and Applications, 3(1), 21-39. · Zbl 1276.62103
[4] Dia, G., 2008. Estimation nonparam´etrique de la distribution des revenus et de l’indice de pauvret´e.C. R. Acad. Sci. Paris, Ser. I 346, 907-912. · Zbl 1147.91043
[5] Foster, J. E. and, Greer, J. and, Thorbecke, E., 1984. A class of decomposable poverty measures.Econometrica, 52, 761-776. · Zbl 0555.90029
[6] Lo, G. S., 2003. Estimation des lois du revenu et des d´epenses dans une base de donn´ees de pauvret´e.Publications de l’UFR-SAT, LERSTAD num. 8 UGB S ´en ´egal.
[7] Lo, G.S., Sall, S.T., and Seck, C.T., 2009. Une th´eorie asymptotique g´en´erale des mesures de pauvret´e.C.R. Math. Rep. Acad. Sci. Canada., 32(2), 45-52. · Zbl 1178.91154
[8] B. Zakaria, Y. Ciss and A. Diakhaby, Afrika Statistika, Vol. 15 (1), 2020, pages2179
[9] 2197. Asymptotic Normality of Non-parametric Estimator for the FGT Poverty Index via
[10] Adaptive Kernel.2197
[11] Parzen1, E., 1962. On estimation of a probability density function and mode.Annals of Mathematical Statistics, Volume 33, Issue 3, 1065-1076. · Zbl 0116.11302
[12] Seck, C. T., 2011. Estimation Non-param´etrique et Convergence Faible des Mesures de Pauvret´e.PhD thesis, Universit ´e Pierre et Marie Curie
[13] Seck, C. T. and, Lo, G. S., 2009. Uniform convergence of the non-weighted poverty measures. Communications in Statistics - Theory and Methods, 38(20), 3697-3704. · Zbl 1186.62135
[14] Seidl, C., 1988. Poverty measurement: a survey, in: D. bos, c. seidl (eds.), welfare and efficienty in public economics.Springer- Verlag, Heidelberg, 71-147.
[15] Silverman, B. W, 1986. Density Estimation for Statistics and Data Analysis.London, Chapman & Hall · Zbl 0617.62042
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