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Asymptotic normality of non-parametric estimator for the FGT poverty index with when the parameter is strictly between 0 and 1. (English. French summary) Zbl 1356.60033

Summary: In this paper, we study the kernel estimator of Foster, Greer and Thorbecke class of measures when the poverty aversion parameter is strictly between zero and one, as a genreralization of the work of G. Dia [J. Math. Sci. Adv. Appl. 3, No. 1, 21–39 (2009; Zbl 1276.62103)]. We solved an open problem arising in mentioned paper. The asymptotic normality of the estimator is established. As an illustration, we determine the confidence intervals for different regions of Senegal. The study of this application demonstrated that our methodology is not only more efficient than the empirical estimator, but it also provides better confidence intervals for the poverty index.

MSC:

60F05 Central limit and other weak theorems
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
91D99 Mathematical sociology (including anthropology)

Citations:

Zbl 1276.62103
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Full Text: Euclid