In this paper, we propose a bi-dimensional extension of the Foster, Greer and Thorbecke index using the adaptive kernel density. The estimator we proposed is based on Riemann sums and the adaptive kernel density. We establish its almost-sure uniform convergence and its uniform mean square consistency.

The performance of the proposed new estimator is evaluated via the variance and the mean squared error. The results of the simulations studies are promising enough to show that our new estimator performs well in all the cases.

poverty line, adaptive kernel, uniform almost sure consistency, uniform mean square consistency, bi-dimensional extension, Riemann sums.

Received: January 8, 2022; Accepted: March 1, 2022; Published: August 27, 2022

How to cite this article: Al Hassana Diallo, Youssou Ciss, Baradine Zakaria and Aboubakary Diakhaby, On the adaptive bi-dimensional kernel density estimation of well-being distribution and poverty index, Far East Journal of Theoretical Statistics 66 (2022), 15-72. http://dx.doi.org/10.17654/0972086322012

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

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