Strategies for exploiting auxiliary information and achieving spatial balance in environmental surveys

In environmental and ecological surveys, estimating totals or functions of totals is typically approached within a design-based framework. Nowadays remote sensing technologies provide a large amount of auxiliary variables, which can be adopted at design or estimation level to improve the precision of estimators. At design level, schemes explicitly tailored to achieve spatial balance can effectively leverage these auxiliary variables. On the other hand, auxiliary variables can be adopted at estimation level both under the explicitly tailored schemes and under straightforward schemes which also ensure spatially balanced samples. An extensive simulation study compares the performances of alternative strategies exploiting auxiliary information at different levels, highlighting the challenges involved in choosing the most suitable auxiliary variables.