Afrika Statistika

Asymptotic Normality of Non-parametric Estimator for the FGT Poverty Index via Adaptive Kernel

Zakaria BARADINE, Youssou CISS, and Aboubakary DIAKHABY

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Abstract

In this paper, we study the kernel estimator of the measurement class of Foster, Greer and Thorbecke to establish the asymptotic normality of the kernel estimator of the FGT poverty index by the adaptive method for the values of \(\alpha = 0\) and \(\alpha \geq 1\). We then provide a performance study of this estimator, on simulated data, compared to the estimator from the non-adaptive kernel and the empirical estimator. The study shows that an adaptive kernel estimator is recommended.

Résumé

Dans ce papier, nous étudions l'estimateur à noyau de la classe de mesure de Foster, Greer et Thorbecke afin établir la normalité asymptotique de l'estimateur à noyau de l'indice de pauvreté FGT par la méthode adaptative pour \(\alpha = 0\) et \(\alpha \geq 1\). A titre d'illustration, nous déterminerons les intervalles de confiance sur des données simulées pour différentes valeurs du seuil de pauvreté. Par cette étude nous montrons que pour la plupart des valeurs du seuil de pauvreté, le nouveau estimateur est non seulement plus efficace que les deux autres estimateurs mais génère des intervalles de confiance d'amplitudes plus petites.

Article information

Source
Afr. Stat., Volume 15, Number 1 (2020), 2179-2197.

Dates
First available in Project Euclid: 16 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.as/1589594486

Digital Object Identifier
doi:10.16929/as/2020.2179.153

Mathematical Reviews number (MathSciNet)
MR4099223

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62G05: Estimation

Keywords
poverty line poverty aversion adaptive kernel Foster, Greer and Thorbecke uniform convergence asymptotic normality

Citation

BARADINE, Zakaria; CISS, Youssou; DIAKHABY, Aboubakary. Asymptotic Normality of Non-parametric Estimator for the FGT Poverty Index via Adaptive Kernel. Afr. Stat. 15 (2020), no. 1, 2179--2197. doi:10.16929/as/2020.2179.153. https://projecteuclid.org/euclid.as/1589594486


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