Kernel Heaping - Kernel Density Estimation from regional aggregates via measurement error model

Freie Universität Berlin, FB Wirtschaftswissenschaft

Freie Universität Berlin, FB Wirtschaftswissenschaft

INWT Statistics GmbH

Freie Universität Berlin, FB Wirtschaftswissenschaft

Abstract

The phenomenon of “aggregation” often occurs in the regional dissemination of information via choropleth maps. Choropleth maps represent areas or regions that have been subdivided and color-coded proportionally to ordinal or scaled quantitative data. By construction discontinuities at the boundaries of rigid aggregation areas, often of administrative origin, occur and inadequate choices of reference areas can lead to errors, misinterpretations and difficulties in the identification of local clusters. However, these representations do not reflect the reality. Therefore, a smooth representation of georeferenced data is a common goal. The use of naive non-parametric kernel density estimators based on aggregates positioned at the centroids of the areas result also in an inadequate representation of reality. Therefore, an iterative method based on the Simulated Expectation Maximization algorithm was implemented in the Kernelheaping package. The proposed approach is based on a partly Bayesian algorithm treating the true unknown geocoordinates as additional parameters and results in a corrected kernel density estimate.

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