The effect of sampling design in model-based small area estimation

It has been shown that simple random sampling is not necessarily the best option, when data is collected for modelling and mapping forest resources. Instead, other sampling designs like systematic or stratified sampling may be better options for those purposes. Furthermore, it has been shown that for stratified sampling, Neyman allocation based on the influence of a given model predictor will produce the smallest estimation error for its coefficient. In this study, we explore if the small-area estimation can be improved by the selection of sampling design, and how that depends on the properties of the small areas. We tested four different sampling designs (simple random sampling, pseudo-systematic sampling, spatially balanced sampling, and stratified sampling) for small area estimation. We also tested two different versions of Neyman allocation: traditional Neyman allocation based on remote sensing variables, and another based on their influences on the estimated regression coefficients. The results show that the model-based small-area estimates were seriously underestimated for the domains with largest volume with all modelling methods, due to the model predictions not capturing exceptionally large values. This could only slightly be alleviated with the choice of a sampling design. On the other hand, the designs weighting the high-end volume domains produced less accurate results for the middle and low-end volume domains. The model-based estimation without field plots for calibrating the model is not capable of identifying the domains with largest values of target variables nor producing unbiased estimates for them. Thus, it is important to develop calibration methods applicable also for non-sampled domains.