Small Area Estimation with a Lognormal Mixed Model under Informative Sampling

Zimmermann Thomas () and Münnich Ralf Thomas ()
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Zimmermann Thomas: Statistisches Bundesamt, Mathematical-Statistical Methods & Research Data Centre, Gustav-Stresemann-Ring 11, D-65189Wiesbaden, Germany.
Münnich Ralf Thomas: University of Trier, Faculty IV – Economics, Economic and Social Statistics Department, Universitätsring 15, D-54286Trier, Germany.

Journal of Official Statistics, 2018, vol. 34, issue 2, 523-542

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.

Keywords: Small area estimation; informative sampling; lognormal mixed model (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:offsta:v:34:y:2018:i:2:p:523-542:n:12

DOI: 10.2478/jos-2018-0024

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