Kernel density estimation under masking of geolocations with applications to DHS data

The availability of geocoordinates offers valuable insights into spatial patterns of economic, demographic and health outcomes. However, disclosing the exact geolocation of statistical units to secondary analysts contravenes the responsible use of data. To protect privacy, anonymisation methods are used. A commonly applied anonymisation method is the one used by Demographic and Health Surveys (DHS). The DHS anonymisation scheme works by first aggregating data at small spatial units followed by random (donut) displacement of the geocoordinates. It is reasonable for secondary analysts to be concerned about the impact of anonymisation on the analyses. In this paper, the DHS anonymisation scheme is used as a basis for studying how anonymisation impacts on kernel density estimation. We propose methodology to account for the impact of the anonymisation process on density estimation. The proposed methodology is based on deriving the distribution of the true coordinates given the observed (anonymised) coordinates. Density estimation is then implemented by using the theoretical distribution and an iterative algorithm that accounts for both aggregation and displacement. The aim is to approximate the original population density using generated pseudo-coordinates under the assumption that the anonymisation process is known. The proposed method is illustrated by using DHS data from the Rajshahi Division in Bangladesh to estimate the density of households below the poverty line. The results show that accounting for measurement error due to anonymisation leads to a more accurate picture of the spatial distribution of poverty.