Afrika Statistika

Asymptotic Normality of Non-parametric Estimator for the FGT Poverty Index with when the parameter is strictly between 0 and 1

Youssou CISS and Aboubakary DIAKHABY

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Abstract

In this paper, we study the kernel estimator of Foster, Greer and Thorbecke class of measures when the poverty aversion parameter is strictly between zero and one, as a genreralization of the work of Dia(2016). We solved an open problem arising in mentioned paper. The asymptotic normality of the estimator is established. As an illustration, we determine the confidence intervals for different regions of Senegal. The study of this application demonstrated that our methodology is not only more efficient than the empirical estimator, but it also provides better confidence intervals for the poverty index.

Abstract

Dans ce papier, nous étudions l'estimateur à noyau de la classe de mesures de Foster, Greer et Thorbecke pour généraliser les résultats de Dia(2016) pour de petites valeurs du paramètre d'aversion, c'est à dire lorsque ce dernier est compris entre 0 et 1 strictement. Ce cas restait un problème ouvert dans le travail de Dia. Nous avons établi la normalité asymptotique de l'estimateur à noyau. A titre d'illustration, nous déterminerons les intervalles de confiance pour les différentes régions du Sénégal. Nous montrons par cette application que l'estimateur proposé est non seulement plus efficace que l'estimateur empirique mais, il produit aussi des intervalles de confiance plus petits de contenant l'indice de pauvreté.

Article information

Source
Afr. Stat., Volume 11, Number 2 (2016), 965-981.

Dates
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.as/1484881310

Digital Object Identifier
doi:10.16929/as/2016.965.87

Mathematical Reviews number (MathSciNet)
MR3599802

Zentralblatt MATH identifier
1356.60033

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

Citation

CISS, Youssou; DIAKHABY, Aboubakary. Asymptotic Normality of Non-parametric Estimator for the FGT Poverty Index with when the parameter is strictly between 0 and 1. Afr. Stat. 11 (2016), no. 2, 965--981. doi:10.16929/as/2016.965.87. https://projecteuclid.org/euclid.as/1484881310


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