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 km(2) 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 (<23 for both attributes) of large size (similar to 15,000 ha) having an average estimation error lower than 7.7% for both attributes. Relaxing the targeted error threshold to 50% led to a larger amount of smaller domains (80 domains of 4,176 ha in average) for both attributes, and maximum estimation errors reaching 42.8%. Among those domains 65% consisted in single municipalities. For the sake of comparison, the estimation was also conducted at the scale of municipalities. Out of the 157 municipalities studied, only 93 were sampled with at least 3 NFI points and therefore estimated. Missing values were generated for the remaining 64 municipalities. Average errors of 15.9% and 15.6% were obtained for growing stock and basal area respectively, but estimation errors greater than 50% were obtained for some municipalities. The algorithm provides a flexible estimation framework for small area estimation. The key advantages of the approach are relying on its capacity to produce estimations based on a preselected precision threshold and to produce results over the whole area of interest, avoiding areas without any estimates. The algorithm could also be used on any kind of polygon layers (not only administrative ones), provided that the field sampling design enable estimation. This makes the proposed algorithm a convenient tool notably for decision makers and forest managers.

Automated summary

Integrating NFI data with auxiliary information enables downscaling and improving precision of estimates for small domains. A downsaling algorithm was tested in a hardwood forest area in France, resulting in improved estimation accuracy.