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Keywords: census, differential privacy, penalized splines
We apply a non-parametric method for smoothing age distributions using P-splines to differentially private population data. We test the approach on demonstration data from the 2010 US Census with age, sex, and race/ethnicity detail. We find that smoothing can reduce the observed differences between a differentially private population dataset and population counts by age as enumerated, preserving important population features without use of privileged information. We discuss implications for data from the 2020 US Census and potential consequences for measurement of a variety of economic, social, and demographic phenomena.