Constrained map-based inventory estimation
A region can conceptually be tessellated into polygons at different scales or resolutions. Likewise, samples can be taken from the region to determine the value of a polygon variable for each scale. Sampled polygons can be used to estimate values for other polygons at the same scale. However, estimates should be compatible across the different scales. Estimates are often required for zones within a region, where a region might be a state and counties could be the zones. A method is developed for estimating high-resolution (pixel) values that are constrained to be compatible with results for lower resolution values. The high-resolution values are constrained to sum to totals for zones within a region, where the totals are being simultaneously estimated from measurements taken 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 constrained to approach unbiased estimates. Approximate variance estimators are developed for the summed pixel estimates. Two example applications are provided. The first example is based on simulated data and verifies that the proposed variance estimators give reasonable results. The second example estimates the volume in a circle around a possible mill site in North Carolina. This example uses publicly available US Forest Service inventory data and simulated inventory data that the mill would provide.