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ON THE ADAPTIVE BI-DIMENSIONAL KERNEL DENSITY ESTIMATION OF WELL-BEING DISTRIBUTION AND POVERTY INDEX
Keywords:
poverty line, adaptive kernel, uniform almost sure consistency, uniform mean square consistency, bi-dimensional extension, Riemann sumsDOI:
https://doi.org/10.17654/0972086322012Abstract
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.
Received: January 8, 2022
Accepted: March 1, 2022
References
Y. Ciss, G. Dia and A. Diakhaby, Bidimensional nonparametric estimation of well-being distribution and poverty index, Afrika Statistika 9 (2014), 695-725.
J. Y. Duclos, D. E. Sahn and S. D. Younger, Robust multidimensional spatial poverty comparisons in Ghana, Madagascar, and Uganda, World Bank Econ. Rev. 20(1) (2006a), 91-113.
J. E. Foster, J. Greer and E. Thorbecke, A class of decomposable poverty measures, Econometrica 52 (1984), 21-39.
E. Parzen, On estimation of a probability density function and mode, Annals of Mathematical Statistics 33(3) (1962), 1065-1076.
B. W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman & Hall, London, 1986.
Baradine Zakaria, Youssou Ciss and Aboubakary Diakhaby, Adaptive kernel density estimation of income distribution and poverty index, A Collection of Papers in Mathematics and Related Sciences: A Festschrift in Honour of the Late Galaye Dia, H. Seydi, G. S. Lo and A. Diakhaby, eds., Spas Editions, Euclid Series Book, 2018, pp. 103-128. Doi: /0.16929/sbs/2018.100-02-04.
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