We propose a class of misaligned data models for addressing typical small area estimation (SAE) problems. In particular, we extend hierarchical Bayesian atom-based models for spatial misalignment to the SAE context enabling use of auxiliary covariates, which are available on areal partitions non nested with the small areas of interest, along with planned domains survey estimates also misaligned with these small areas. We model the latent characteristic of interest at atom level as a Poisson variate with mean arising as a product of population size and incidence. Spatial random effects are introduced either using a CAR model or a process specification.For the latter, incidence is a function of a Gaussian process model for the spatial point pattern over the entire region. Atom counts are driven by integrating the point process over atoms. In the proposed class of models benchmarking to large area estimates is automatically satisfied. A simulation study examines the capability of the proposed models to improve on traditional SAE model estimates.
