Asymptotic normality of non-parametric estimator for the FGT poverty index with when the parameter is strictly between 0 and 1

Abstract

Abstract. 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 generalization of the work of Dia (2009). We solved an open problem arising in mentioned paper. The asymptotic normality of the estimator is established. As an illustration, we determine the condence intervals for dierent 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 condence intervals for the poverty index.

Key words: Poverty line; Poverty aversion; Moving kernel; Foster; Greer and Thorbecke; Uniform convergence; Asymptotic normality.