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Open access

Sabine Krieg, Harm Jan Boonstra and Marc Smeets

Abstract

Many target variables in official statistics follow a semicontinuous distribution with a mixture of zeros and continuously distributed positive values. Such variables are called zero inflated. When reliable estimates for subpopulations with small sample sizes are required, model-based small-area estimators can be used, which improve the accuracy of the estimates by borrowing information from other subpopulations. In this article, three small-area estimators are investigated. The first estimator is the EBLUP, which can be considered the most common small-area estimator and is based on a linear mixed model that assumes normal distributions. Therefore, the EBLUP is model misspecified in the case of zero-inflated variables. The other two small-area estimators are based on a model that takes zero inflation explicitly into account. Both the Bayesian and the frequentist approach are considered. These small-area estimators are compared with each other and with design-based estimation in a simulation study with zero-inflated target variables. Both a simulation with artificial data and a simulation with real data from the Dutch Household Budget Survey are carried out. It is found that the small-area estimators improve the accuracy compared to the design-based estimator. The amount of improvement strongly depends on the properties of the population and the subpopulations of interest.

Open access

Reinier Bikker, Jan van den Brakel, Sabine Krieg, Pim Ouwehand and Ronald van der Stegen

Abstract

Seasonally adjusted series of Gross Domestic Product (GDP) and its breakdown in underlying categories or domains are generally not consistent with each other. Statistical differences between the total GDP and the sum of the underlying domains arise for two reasons. If series are expressed in constant prices, differences arise due to the process of chain linking. These differences increase if, in addition, a univariate seasonal adjustment, with for instance X-13ARIMA-SEATS, is applied to each series separately. In this article, we propose to model the series for total GDP and its breakdown in underlying domains in a multivariate structural time series model, with the restriction that the sum over the different time series components for the domains are equal to the corresponding values for the total GDP. In the proposed procedure, this approach is applied as a pretreatment to remove outliers, level shifts, seasonal breaks and calendar effects, while obeying the aforementioned consistency restrictions. Subsequently, X-13ARIMA-SEATS is used for seasonal adjustment. This reduces inconsistencies remarkably. Remaining inconsistencies due to seasonal adjustment are removed with a benchmarking procedure.