Research Article
Bivariate Radialsymmetric Kernel Density Estimation of Well-being Distribution and Poverty Index
Youssou Ciss
,
Mamadou Djitan Sinclair,
Mohamed Dinah Bangoura,
Aboubakary Diakhaby
Issue:
Volume 15, Issue 5, October 2026
Pages:
177-201
Received:
9 June 2026
Accepted:
24 July 2026
Published:
5 September 2026
DOI:
10.11648/j.ajtas.20261505.11
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Abstract: In two previous papers, we proposed two bivariate product kernel estimators for the bi-dimensional extension of the Foster, Greer and Thorbecke (FGT) index based respectively on classical and adaptive kernel. The Foster, Greer and Thorbecke (FGT) index was introduced in the literature for the purpose of a dominance approach to multidimensional poverty. The poverty measure utilized in this dominance method is fundamentally a generalization, from one to two dimensions, of this Foster, Greer and Thorbecke index with separate poverty aversion parameters for each dimension. This statistical method (the product kernel estimator) has the following main disadvantes: the curse of dimensionality, the complex selection of the bandwidth, and high computational costs. In this study, we focus on a bivariate radialsymmetric kernel estimator for the bi-dimensional extension of the Foster, Greer and Thorbecke index. Our new bivariate kernel estimator is developed with a classical bivariate kernel of Parzen-Rosenblatt of a probability density function (pdf) utilizing Riemann sums. We next provide complete asymptotic behaviour by establishing both almost-sure uniform and uniform mean square consistencies for the bivariate radialsymmetric kernel estimator. A simulation study indicates that the proposed bivariate kernel estimator performs favorably for small samples comparatively to the bivariate multiplicative kernel estimator.
Abstract: In two previous papers, we proposed two bivariate product kernel estimators for the bi-dimensional extension of the Foster, Greer and Thorbecke (FGT) index based respectively on classical and adaptive kernel. The Foster, Greer and Thorbecke (FGT) index was introduced in the literature for the purpose of a dominance approach to multidimensional pov...
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