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

Small-Area Estimation with Zero-Inflated Data – a Simulation Study

Statistics Netherlands, Postbus 4481, 6401CZ Heerlen,

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Small-Area Estimation with Zero-Inflated Data \u2013 a Simulation Study"}

Many target variables in official statistics follow a semicontinuous distribution with a mixture of zeros and continuously distributed positive values. Such...

Small-Area Estimation with Zero-Inflated Data – a Simulation Study

Article Category: Articles

Publié en ligne: 23 nov. 2016

Pages: 963 - 986

Reçu: 01 mars 2015

Accepté: 01 août 2016

DOI: https://doi.org/10.1515/jos-2016-0051

Mots clés
Generalized linear mixed model, EBLUP, MCMC, Logit, Dutch Household Budget Survey

© by Sabine Krieg

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Small-Area Estimation with Zero-Inflated Data – a Simulation Study

Article Category: Articles

Publié en ligne: 23 nov. 2016

Pages: 963 - 986

Reçu: 01 mars 2015

Accepté: 01 août 2016

DOI: https://doi.org/10.1515/jos-2016-0051

Mots clésGeneralized linear mixed model, EBLUP, MCMC, Logit, Dutch Household Budget Survey

© by Sabine Krieg

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Generalized linear mixed model, EBLUP, MCMC, Logit, Dutch Household Budget Survey