Estimating the Density of Ethnic Minorities and Aged People in Berlin: Multivariate Kernel Density Estimation Applied to Sensitive Georeferenced Administrative Data Protected Via Measurement Error

Abstract

Modern systems of official statistics require the timely estimation of area-specific densities of subpopulations. Ideally estimates should be based on precise geocoded information, which is not available because of confidentiality constraints. One approach for ensuring confidentiality is by rounding the geoco-ordinates. We propose multivariate non-parametric kernel density estimation that reverses the rounding process by using a 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.

Switching Between Different Non-Hierachical Administrative Areas via Simulated Geo-Coordinates: A Case Study for Student Residents in Berlin

“…The generation of the pseudo-sample step brings a stochastic element into the algorithm, giving a more realistic distribution of the missing observations. In our application, the missing data are the exact geo-coordinates and the maximization of a likelihood is replaced by the kernel density estimation (a generalised SEM, Groß et al 2017). In contrast to SEM, a simple EM algorithm would clearly not be helpful in this application, as all observations within an area would fall on the same location and thus not prevent a bias of the resulting kernel density estimate.…”

“…Therefore, we present an approach in which geo-coordinates are simulated from area-specific aggregates. The method proposed in this work is similar to the approach of Groß et al (2017), where it is used to counteract the rounding of geo-coordinates due to confidentiality reasons. In their analysis, kernel densities are generated to detect concentration areas of migrants and elderly persons in Berlin.…”

How Is the Confidentiality of Crime Locations Affected by Parameters in Kernel Density Estimation?

“…To avoid such problems, various types of location protecting techniques have been used to protect these privacies [4,5,9,11,13,14]. Geocoding of crime events to a street segment or a city block can encrypt their precise geographic locations [4][5][6]. Transforming a point map to a density map can help mask the exact location of crime events [4,5,11,16,39].…”

“…Kernel density estimation (KDE) is widely adopted to show the overall crime distribution and at the same time obscure exact crime locations due to the confidentiality of crime data in many countries [1][2][3][4][5][6]. In the field of crime prediction, KDE is widely used to generate hotspots, which are then used to guide police for targeted intervention.…”

Kernel Density Estimation for Heaped Data

“…As a consequence, the proposed estimator is a partly Bayesian method in the sense that the X i as well as p, a, β and τ are treated as random variables but not θ. As already discussed in Groß et al (2015) this approach is equal to a generalized Stochastic Expectation Maximization (SEM) algorithm (Celeux et al 1996). This algorithm is strongly related to the Gibbs-sampler but usually converges much faster (Diebolt et al 1994).…”