Simulation studies to examine bias and precision of some estimators that use auxiliary information in design-based sampling in forest inventory

Background: Various double sampling methods using both target and auxiliary variables have been developed over many years for use in natural resource inventory. Methods: Simulations of inventory were carried out using four different ratio estimators and model-assisted estimation in each of five rather different example forest populations. Estimates of population means and their standard errors from each of these methods were compared with those obtained using simple random sampling. Results: With all five double sampling estimators, bias in estimates of means and standard errors (the latter estimated analytically or through bootstrapping) was generally small and consistent with theoretical expectations. Their efficiency increased as either the first- or second-phase sample sizes increased. All were more efficient than estimates obtained using simple random sampling as long as there was some positive level of correlation between the target and auxiliary variable. However, none of the double sampling estimators was more efficient than any of the others. Conclusions: For many forest inventory tasks, users may well be able to use whichever of the estimators is most convenient to their purpose. However, model-assisted estimation has application in a wider range of circumstances than the other methods, which perhaps recommends it for general use.