Interpolating Distributions for Populations in Nested Geographies using Public-use Data with Application to the American Community Survey.

Statistical agencies often publish multiple data products from the samesurvey. First, they produce aggregate estimates of various features of thedistributions of several socio-demographic quantities of interest. Often thesearea-level estimates are tabulated at small geographies. Second, statisticalagencies frequently produce weighted public-use microdata samples (PUMS) thatprovide detailed information of the entire distribution for the samesocio-demographic variables. However, the public-use micro areas usuallyconstitute relatively large geographies in order to protect against theidentification of households or individuals included in the sample. These twodata products represent a trade-off in official statistics: publicly availabledata products can either provide detailed spatial information or detaileddistributional information, but not both. We propose a model-based method tocombine these two data products to produce estimates of detailed features of agiven variable at a high degree of spatial resolution. Our motivating exampleuses the disseminated tabulations and PUMS from the American Community Surveyto estimate U.S. Census tract-level income distributions and statisticsassociated with these distributions.