Numerical experiments with the thin plate histospline

The thin plate volume matching and volume smoothing histosplines are described. These histosplines are suitable for estimating densities or incidence rates as a function of position on the plane when data is aggregated by area, for example by county. We give a numerical algorithm for the volume matching histospline and for the volume smoothing histospline using generalized cross validation to estimate the smoothing parameter. Some numerical experiments were performed using synthetic data, population data and SMR's (standardized mortality ratios) aggregated by county over the state of Wisconsin. The method turns out to be not particularly suited for obtaining population density maps where the population density can vary by two orders of magnitude, because the histospline can be negative in