When collecting geocoded confidential data with the intent to disseminate,agencies often resort to altering the geographies prior to making data publiclyavailable due to data privacy obligations. An alternative to releasingaggregated and/or perturbed data is to release multiply-imputed synthetic data,where sensitive values are replaced with draws from statistical models designedto capture important distributional features in the collected data. One issuethat has received relatively little attention, however, is how to handlespatially outlying observations in the collected data, as common spatial modelsoften have a tendency to overfit these observations. The goal of this work isto bring this issue to the forefront and propose a solution, which we refer toas "differential smoothing." After implementing our method on simulated data,highlighting the effectiveness of our approach under various scenarios, weillustrate the framework using data consisting of sale prices of homes in SanFrancisco.
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