Constrained map-based inventory estimation

A region can conceptually be tessellated into polygons at differentscales or resolutions. Likewise, samples can be taken from theregion to determine the value of a polygon variable for eachscale. Sampled polygons can be used to estimate values for otherpolygons at the same scale. However, estimates should be compatibleacross the different scales. Estimates are often required forzones within a region, where a region might be a state and countiescould be the zones. A method is developed for estimating high-resolution(pixel) values that are constrained to be compatible with resultsfor lower resolution values. The high-resolution values areconstrained to sum to totals for zones within a region, wherethe totals are being simultaneously estimated from measurementstaken at a different scale. If the zone estimates are unbiased,then the pixel-based estimates for the zone will be less biased.Sums of pixels in arbitrary polygons are thereby constrainedto approach unbiased estimates. Approximate variance estimatorsare developed for the summed pixel estimates. Two example applicationsare provided. The first example is based on simulated data andverifies that the proposed variance estimators give reasonableresults. The second example estimates the volume in a circlearound a possible mill site in North Carolina. This exampleuses publicly available US Forest Service inventory data andsimulated inventory data that the mill would provide.