A new small area estimation algorithm to balance between statistical precision and scale

Combining national forest inventory (NFI) data with auxiliary information allows downscaling and improving the precision of NFI estimates for small domains, where normally too few field plots are available to produce reliable estimates. In most situations, small domains represent administrative units that could greatly vary in size and forested area. In small and poorly sampled domains, the precision of estimates often drop below expected standards.To tackle this issue, we introduce a downscaling algorithm generating the smallest possible groups of domains satisfying prescribed sampling density and estimation error. The binary space partitioning algorithm recursively divides the population of domains in two groups while the prescribed precision conditions are fulfilled.The algorithm was tested on two major forest attributes (i.e. growing stock and basal area) in an area of 7,500 km2 dominated by hardwood forests in the centre of France. The estimation domains consisted in 157 municipalities. The field data included 819 NFI plots surveyed during a 5 years period. The auxiliary data consisted in 48 metrics derived from a forest map, photogrammetric models and Landsat images. A model-assisted framework was used for estimation. For each forest attribute, the best model was selected using a best-subset approach using a Bayesian Information Criteria. The retained models explained 58% and 41% of the observed variance for the growing stocks and basal areas respectively. The performance of the algorithm was evaluated using a minimum of 3 NFI points per domain and estimation errors varying from 10 to 50%.For a target estimation error set to 10%, the algorithm led to a limited number of estimation domains (