Double sampling with importance sampling to eliminate bias in tree volume estimation of the centroid method

Abstract

The bias associated with the centroid method for estimating tree volume was removed by double sampling using the centroid method in the first stage of estimation and importance sampling in the second. The bias and efficiency of various sampling methods were investigated in a number of different simulation studies. Three data sets, two of ponderosa pine and the other of mixed species, were used to evaluate the double sampling estimator. We assumed that for small area estimates, such as timber sales, every tree in the population could be visited in the first stage and an estimate of bole volume generated using the centroid method. Both simple random and 3P sampling were studied as methods for selecting the second-stage sample trees. For the estimation of volume over a large area, we chose point-3P sampling for applying the double sampling estimator. The bias associated with using the centroid method alone was reduced in every case. No consistent trends for the three data sets were found when efficiency was measured in terms of the simulation variance. The double sampling estimator was the most efficient in some cases and least efficient in others.