Bidimensional non-parametric estimation of well-being distribution and poverty index

In this paper, we introduce a kernel-type version for the bi-dimensional extension of the Foster, Greer, and Thorbecke index that was introduced by Duclos et al. (2006a) for the purpose of a dominance approach to multidimensional poverty. The measure they used in their dominance exercise is essentially a generalization, from one to two dimensions, of the FGT index with separate poverty aversion parameters for each dimension. Our estimator is constructed by using a bidimensional Parzen-Rosenblatt kernel of a probability density function (pdf). We next provide its complete asymptotic behaviour by establishing its almost- sure uniform and its uniform mean square consistencies. A simulation study shows that it performs well for small samples comparatively to the empirical plug-in estimator. Our results are also extensions of those of Dia (2008) and of Ciss et al. (2014) in one dimension. R