Forest inventory with optimal two-phase two-stage sampling schemes based on the anticipated variance

This work presents optimal sampling schemes for forest inventory. The sampling procedures are optimal in the sense that they minimize the anticipated variance for given costs or conversely, the anticipated variance is the average of the design-based variance under a local Poisson model for the spatial distribution of the trees. The resulting optimal inclusion rules are either probability proportional to size, in one-stage procedures, or a combination of probability proportional to prediction and probability proportional to error, in two-stage procedures. Best feasible approximations of the exact optimal sampling schemes are also given.