Enhancing inference for spatial populations: the use of remotely sensed data in sampling strategies

The development and diffusion of tools such as satellites, drones, and other systems that collect wall-to-wall information across a territory provide valuable information on statistical units. Often, this information does not directly answer the specific questions under study and/or could be influenced by measurement errors or self-selection bias. Nevertheless, it can be effectively used as an auxiliary variable for an ad hoc survey, allowing for more cost-efficient estimates of the target variable. Our study focuses on investigating the different uses of remotely sensed data as auxiliary variables in sampling strategies for spatially distributed populations. To do so, we cannot disregard the specific characteristics of geographical phenomena, which commonly exhibit spatial patterns and an uneven distribution across populations. In such cases, it is known in the literature that spatially balanced samples allow for the collection of more information, leading to more accurate estimates of a mean or total for a target variable. Therefore, even when it is possible to implement a sampling strategy that relies on auxiliary information, either in the design or estimation phases, such a strategy should still spread the sample units in space as well. Choosing a sampling strategy must take into account two key factors. First, in the context of spatially related data, the relationship between the study and auxiliary variables may be partially or wholly influenced by spatial covariability. Second, the exact relationship between the target and auxiliary variables is never fully known. To address these challenges, Bocci et al. (2024) proposed a sampling strategy that involves a two-step spatially balanced sampling process. In the first step, this strategy evaluates the potential benefits of using auxiliary data in the sampling design. If this data proves to be useful, it is then incorporated in the second step. Here, we suggest extending their two-step sampling strategy by evaluating, at the first step, whether exploiting the auxiliary information in the estimation phase would be advantageous, in addition, or substitution to its use in the design phase. Results from an extensive simulation study indicate that the optimal use of auxiliary information depends on the characteristics of the auxiliary and study variables and their relationship, which is usually not known a priori and needs to be assessed during the sampling procedure itself.