Empirical error analysis in demographic variable approximation for non-standard geographical hierarchies

We revisit three methods for demographic data approximation based on decennial United States Census data: population-weighted interpolation, in-or-out block group assignment, and the trapezoid approximation. We offer rigorous definitions of each method and compare the errors produced using a variety of numerical experiments. We conclude that population-weighted interpolation, while more computationally taxing, produces better estimates for smaller geographical areas with the three methods converging for larger polygons.