Potential for wider application of 3P sampling in forest inventory

Sampling with probability proportional to prediction (3P sampling) is useful where the variable of interest to a forest inventory is costly to measure and where there exists a cheaper to measure auxiliary variable, which correlates positively with the variable of interest. Two forms of 3P sampling, termed 'classical' and 'point-' 3P sampling, have received some use in forest inventory. However, both have limitations that have restricted their use mainly to estimation of tree stem wood volume for timber sales over small forest areas in North America. A more general form of 3P sampling, termed here 'ordinary' 3P sampling, has been all but ignored to date. It has potential for use in inventory of a broad range of forest attributes, both floral and faunal and both commercial and environmental, across large or small forest areas. Using a common mathematical approach, the present work derives the estimators of the population mean for these three forms of 3P sampling. Their properties are compared with simple random sampling through Monte Carlo simulations based on two example forest populations. The work lays a basis from which 3P sampling might develop further and enjoy wider application in forest inventory than has been the case previously.