Multivariate applications of the ash in regression

A simple algorithm for estimating the regression function over the United States is introduced. The approach allows for data obtained from a complicated sampling design, as well as for the inclusion of a few additional covariates. The regression estimates are obtained from an associated probability density estimate, namely the averaged shifted histogram. The algorithm has proven especially successful over a large mesh, say 300 by 200 nodes, in a data rich setting, even on a 486 computer running Splus. We currently run much higher resolution meshes on a Pentium. Commonly available alternative codes including kriging failed to produce useful estimates in this setting.