Outlier robust domain estimation for business survey data

Outliers are a fact of life for any survey, and especially so for business surveys. If outliers are a concern for estimation of population quantities, it is safe to say that they are even more of a concern in small area estimation, where sample sizes are considerably smaller and model-dependent estimation is the norm. It is therefore of interest to see how outlier robust survey estimation can be adapted to this situation. The development of outlier robust small area methodologies has been the focus of recent small area literature. We review a range of outlier robust small area methodologies and apply these to business survey data from the Netherlands. We discuss both point and Mean Squared Error estimation (MSE) using analytic and bootstrap-type MSE estimators. Finally, we place some emphasis on providing practical guidelines to the survey practitioner for working with outlier robust small area methodologies.