On the Estimation of Smooth Maps from Regional Aggregates via Measurement Error Models: A Review

The contribution discusses the problems associated with generating maps that display local case numbers or local ratios for a system of areas, such as counties. Traditional maps, like choropleths, are discontinuous at borderlines of reference areas, making it difficult to identify local clusters. To overcome this issue, a two-dimensional kernel density estimator delivers a smooth regional distribution of the variable of interest without discontinuity. Due to confidentiality constraints, precise geo-coded information is not available, which ideally should be used for producing the density estimates. Therefore, we describe an algorithm used to generate a kernel density estimate from a set of area aggregates, which is used in several applications in the contribution. These applications include the construction of service maps for childcare, the transfer of student residences from ZIP-code aggregates to administrative area aggregates, the analysis of voting data, and the display of corona-incidence maps. Finally, we discuss the extension of this approach to other areas such as anonymization of geo-coded data and small area estimation.