Estimating the density of ethnic minorities and aged people in Berlin: Multivariate kernel density estimation applied to sensitive geo-referenced administrative data protected via measurement error

Modern systems of official statistics require the timely estimation of area-specific densities of sub-populations. Ideally estimates should be based on precise geo-coded information, which is not available due to confidentiality constraints. One approach for ensuring confidentiality is by rounding the geo-coordinates. We propose multivariate non-parametric kernel density estimation that reverses the rounding process by using a Bayesian measurement error model. The methodology is applied to the Berlin register of residents for deriving density estimates of ethnic minorities and aged people. Estimates are used for identifying areas with a need for new advisory centres for migrants and infrastructure for older people.