<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The demand for reliable business statistics at disaggregated levels, such as industry classes, increased considerably in recent years. Owing to small sample sizes for some of the domains, design-based methods may not provide estimates with adequate precision. Hence, modelbased small area estimation techniques that increase the effective sample size by borrowing strength are needed. Business data are frequently characterised by skewed distributions, with a few large enterprises that account for the majority of the total for the variable of interest, for example turnover. Moreover, the relationship between the variable of interest and the auxiliary variables is often non-linear on the original scale. In many cases, a lognormal mixed model provides a reasonable approximation of this relationship. In this article, we extend the empirical best prediction (EBP) approach to compensate for informative sampling, by incorporating design information among the covariates via an augmented modelling approach. This gives rise to the EBP under the augmented model. We propose to select the augmenting variable based on a joint assessment of a measure of predictive accuracy and a check of the normality assumptions. Finally, we compare our approach with alternatives in a model-based simulation study under different informative sampling mechanisms.</p></abstract>

The demand for reliable business statistics at disaggregated levels, such as industry classes, increased considerably in recent years. Owing to small sample sizes for some of the domains, design-based methods may not provide estimates with adequate precision. Hence, modelbased small area estimation techniques that increase the effective sample size by borrowing strength are needed. Business data are frequently characterised by skewed distributions, with a few large enterprises that account for the majority of the total for the variable of interest, for example turnover. Moreover, the relationship between the variable of interest and the auxiliary variables is often non-linear on the original scale. In many cases, a lognormal mixed model provides a reasonable approximation of this relationship. In this article, we extend the empirical best prediction (EBP) approach to compensate for informative sampling, by incorporating design information among the covariates via an augmented modelling approach. This gives rise to the EBP under the augmented model. We propose to select the augmenting variable based on a joint assessment of a measure of predictive accuracy and a check of the normality assumptions. Finally, we compare our approach with alternatives in a model-based simulation study under different informative sampling mechanisms.

Small Area Estimation with a Lognormal Mixed Model under Informative Sampling

Faculty IV – Economics, Economic and Social Statistics Department

Journal of Official Statistics

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

{"article-title":"Small Area Estimation with a Lognormal Mixed Model under Informative Sampling"}

The demand for reliable business statistics at disaggregated levels, such as industry classes, increased considerably in recent years. Owing to small sample...

Small Area Estimation with a Lognormal Mixed Model under Informative Sampling

Published Online: Jun 07, 2018

Page range: 523 - 542

Received: Oct 01, 2016

Accepted: Oct 01, 2017

DOI: https://doi.org/10.2478/jos-2018-0024

Keywords
Small area estimation, informative sampling, lognormal mixed model

© 2018 Thomas Zimmermann et al., published by Sciendo

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

Small Area Estimation with a Lognormal Mixed Model under Informative Sampling

Published Online: Jun 07, 2018

Page range: 523 - 542

Received: Oct 01, 2016

Accepted: Oct 01, 2017

DOI: https://doi.org/10.2478/jos-2018-0024

KeywordsSmall area estimation, informative sampling, lognormal mixed model

© 2018 Thomas Zimmermann et al., published by Sciendo

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

Keywords
Small area estimation, informative sampling, lognormal mixed model