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Open access

Thomas Zimmermann and Ralf Thomas Münnich


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.

Open access

Jan Pablo Burgard, Ralf Münnich and Thomas Zimmermann


Evidence-based policy making and economic decision making rely on accurate business information on a national level and increasingly also on smaller regions and business classes. In general, traditional design-based methods suffer from low accuracy in the case of very small sample sizes in certain subgroups, whereas model-based methods, such as small area techniques, heavily rely on strong statistical models.

In small area applications in business statistics, two major issues may occur. First, in many countries business registers do not deliver strong auxiliary information for adequate model building. Second, sampling designs in business surveys are generally nonignorable and contain a large variation of survey weights.

The present study focuses on the performance of small area point and accuracy estimates of business statistics under different sampling designs. Different strategies of including sampling design information in the models are discussed. A design-based Monte Carlo simulation study unveils the impact of the variability of design weights and different levels of aggregation on model- versus design-based estimation methods. This study is based on a close to reality data set generated from Italian business data.