Modelling over and undercounts for design-based Monte Carlo studies in small area estimation: An application to the German register-assisted census

In a register-assisted census, the main information about the population is obtained from population registers. Additionally, a sample is drawn to allow for the estimation of population counts for variables that are not included in the registers. Typically, registers suffer from over and undercounts. The over and undercounts are not observable from the register itself. In order to evaluate relevant estimation strategies to deal with over and undercounts, a reliable data set is to be used within a comprehensive Monte Carlo simulation study. This allows for comparing different estimators in a close-to-reality framework. The reliability of the data set is crucial and thus also the correct implementation of over and undercount structures. The impact of different over and undercounts modelling strategies on the prediction of the total population in considerably small regions within a register-assisted census framework is shown.