<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Robust Estimation of the Theil Index and the Gini Coeffient 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...

Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas

Published Online: Dec 26, 2021

Page range: 955 - 979

Received: Oct 01, 2019

Accepted: Jan 01, 2021

DOI: https://doi.org/10.2478/jos-2021-0041

Keywords
Small area estimation, M-quantile models, inequality indicators

© 2020 Stefano Marchetti et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas

Published Online: Dec 26, 2021

Page range: 955 - 979

Received: Oct 01, 2019

Accepted: Jan 01, 2021

DOI: https://doi.org/10.2478/jos-2021-0041

KeywordsSmall area estimation, M-quantile models, inequality indicators

© 2020 Stefano Marchetti et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Small area estimation, M-quantile models, inequality indicators