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

<p>The estimation of poverty and inequality indicators based on survey data is trivial as long as the variable of interest (e.g., income or consumption) is measured on a metric scale. However, estimation is not directly possible, using standard formulas, when the income variable is grouped due to confidentiality constraints or in order to decrease item nonresponse. We propose an iterative kernel density algorithm that generates metric pseudo samples from the grouped variable for the estimation of indicators. The corresponding standard errors are estimated by a non-parametric bootstrap that accounts for the additional uncertainty due to the grouping. The algorithm enables the use of survey weights and household equivalence scales. The proposed method is applied to the German Microcensus for estimating the regional distribution of poverty and inequality in Germany.</p>
</abstract>

The estimation of poverty and inequality indicators based on survey data is trivial as long as the variable of interest (e.g., income or consumption) is measured on a metric scale. However, estimation is not directly possible, using standard formulas, when the income variable is grouped due to confidentiality constraints or in order to decrease item nonresponse. We propose an iterative kernel density algorithm that generates metric pseudo samples from the grouped variable for the estimation of indicators. The corresponding standard errors are estimated by a non-parametric bootstrap that accounts for the additional uncertainty due to the grouping. The algorithm enables the use of survey weights and household equivalence scales. The proposed method is applied to the German Microcensus for estimating the regional distribution of poverty and inequality in Germany.

Iterative Kernel Density Estimation Applied to Grouped Data: Estimating Poverty and Inequality Indicators from the German Microcensus

Journal of Official Statistics

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

The estimation of poverty and inequality indicators based on survey data is trivial as long as the variable of interest (e.g., income or consumption) is...

Iterative Kernel Density Estimation Applied to Grouped Data: Estimating Poverty and Inequality Indicators from the German Microcensus

Published Online: Jun 14, 2022

Page range: 599 - 635

Received: Jun 01, 2020

Accepted: Feb 01, 2022

DOI: https://doi.org/10.2478/jos-2022-0027

Keywords
Direct estimation, Interval-censored data, non-parametric estimation, OECD scale, prediction

© 2022 Paul Walter et al., published by Sciendo

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

Iterative Kernel Density Estimation Applied to Grouped Data: Estimating Poverty and Inequality Indicators from the German Microcensus

Published Online: Jun 14, 2022

Page range: 599 - 635

Received: Jun 01, 2020

Accepted: Feb 01, 2022

DOI: https://doi.org/10.2478/jos-2022-0027

KeywordsDirect estimation, Interval-censored data, non-parametric estimation, OECD scale, prediction

© 2022 Paul Walter et al., published by Sciendo

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

Keywords
Direct estimation, Interval-censored data, non-parametric estimation, OECD scale, prediction