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Robust estimation of the Theil index and the Gini coefficient for small areas

Robust estimation of the Theil index and the Gini coefficient for small areas
Robust estimation of the Theil index and the Gini coefficient for small areas
Small area estimation is receiving considerable attention due to the high demand for small area statistics. Small area estimators of means and totals have been widely studied in the literature. Moreover, in the last years also small area estimators of quantiles and poverty indicators have been studied. In contrast, small area estimators of inequality indicators, which are often used in socio-economic studies, have received less attention. In this article we propose a robust method based on the M-quantile regression model for small area estimation of the Theil index and the Gini coefficient, two popular inequality measures. To estimate the mean squared error a non-parametric bootstrap is adopted. A robust approach is used because often inequality is measured using income or consumption data, which are often non-normal and affected by outliers. The proposed methodology is applied to income data to estimate the Theil index and the Gini coefficient for small domains in Tuscany (provinces by age groups), using survey and Census micro-data as auxiliary variables. In addition, a design-based simulation is carried out to study the behaviour of the proposed robust estimators. The performance of the bootstrap mean squared error estimator is also investigated in the simulation study
0282-423X
Marchetti, Stefano
121df5a9-737f-45fa-9c4a-dddb80c5d450
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Marchetti, Stefano
121df5a9-737f-45fa-9c4a-dddb80c5d450
Tzavidis, Nikolaos
431ec55d-c147-466d-9c65-0f377b0c1f6a

Marchetti, Stefano and Tzavidis, Nikolaos (2021) Robust estimation of the Theil index and the Gini coefficient for small areas. Journal of Official Statistics. (doi:10.2478/jos-2021-0041).

Record type: Article

Abstract

Small area estimation is receiving considerable attention due to the high demand for small area statistics. Small area estimators of means and totals have been widely studied in the literature. Moreover, in the last years also small area estimators of quantiles and poverty indicators have been studied. In contrast, small area estimators of inequality indicators, which are often used in socio-economic studies, have received less attention. In this article we propose a robust method based on the M-quantile regression model for small area estimation of the Theil index and the Gini coefficient, two popular inequality measures. To estimate the mean squared error a non-parametric bootstrap is adopted. A robust approach is used because often inequality is measured using income or consumption data, which are often non-normal and affected by outliers. The proposed methodology is applied to income data to estimate the Theil index and the Gini coefficient for small domains in Tuscany (provinces by age groups), using survey and Census micro-data as auxiliary variables. In addition, a design-based simulation is carried out to study the behaviour of the proposed robust estimators. The performance of the bootstrap mean squared error estimator is also investigated in the simulation study

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Robust_estimation_for_small_area_Theil_index_and_Gini_coefficient - Accepted Manuscript
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Accepted/In Press date: 27 January 2021
Published date: December 2021

Identifiers

Local EPrints ID: 446777
URI: http://eprints.soton.ac.uk/id/eprint/446777
ISSN: 0282-423X
PURE UUID: ba42df98-adaf-4a3c-851e-2556e4b1263b
ORCID for Nikolaos Tzavidis: ORCID iD orcid.org/0000-0002-8413-8095

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Date deposited: 22 Feb 2021 17:32
Last modified: 17 Mar 2024 06:18

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Author: Stefano Marchetti

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