Spatial Smoothing of Geographically Aggregated Data, with Application to the Construction of Incidence Maps

Abstract We address the commonly encountered situation in spatial statistics where data such as counts of incidences of a certain disease are available only in geographically aggregated form. We develop fairly general models and propose a modified version of the locally weighted least squares method to recover the unknown smooth spatial function that is assumed to generate the observations. In the special case of count data, the target function is the intensity function, conditional on the total number of observations. Our method avoids the arbitrariness of selecting a point within each geographic area at which the measurement for the whole area is supposed to be located. We derive basic asymptotic properties, and apply our methods to acquired immune deficiency syndrome (AIDS) incidence data in San Francisco for 1980–1992, where counts are available aggregated over zip code areas.

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