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

Krieg Sabine (), Boonstra Harm Jan () and Smeets Marc ()
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Krieg Sabine: Statistics Netherlands, Postbus 4481, 6401CZ Heerlen, Netherlands
Boonstra Harm Jan: Statistics Netherlands, Postbus 4481, 6401CZ Heerlen, Netherlands
Smeets Marc: Statistics Netherlands, Postbus 4481, 6401CZ Heerlen, Netherlands

Journal of Official Statistics, 2016, vol. 32, issue 4, 963-986

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.

Keywords: Generalized linear mixed model; EBLUP; MCMC; Logit; Dutch Household Budget Survey (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:offsta:v:32:y:2016:i:4:p:963-986:n:13

DOI: 10.1515/jos-2016-0051

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