Chapter On the use of auxiliary information in spatial sampling

Abstract

Technology development has led to a growing availability of low-cost data ready-to-use, frequently derived from large scale observations (i.e. data from pervasive systems like GPS sensors, or remote sensing data from earth observation technologies). Oftentimes, these data can’t directly answer specific questions posed by researchers and data users, or even if they can they are subject to measurement errors or self-selection bias. In both cases it is still necessary to rely, at least partially, on ad-hoc probabilistic surveys. On the other hand, the precision and quality of surveys estimates can be improved by using the data derived from these new sources as auxiliary information in the design phase and/or in the estimation phase. We present a sequential sampling strategy, suitable to investigate a spatially-related phenomenon, which exploits the auxiliary information at design level in order to obtain efficient estimates when the relation between the auxiliary and study variables it is not completely known and/or is not univocally defined for the whole population under study. Using this strategy the final sample is obtained after two (or more) steps: (i) in the first step we collect an initial sample of observations on the target variable, which is used also to investigate the relation between the auxiliary and study variables; (ii) then, this relation is exploited to target and tailor the subsequent sampling step; (iii) additional steps can be included by applying the procedure iteratively. The performance of the suggested strategy is investigated through Monte Carlo experiments by considering several scenarios, which differ in the distributions of the auxiliary and study variables and in their relation.